id stringlengths 31 70 | setting_key stringclasses 31 values | difficulty stringclasses 1 value | level int64 1 1 | messages listlengths 1 1 | ground_truth stringlengths 1 19 | dataset stringclasses 1 value | omega_split stringclasses 1 value | __index_level_0__ int64 0 160k |
|---|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_1_1_0 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(-2sin(1πx - 2) + 2) - 2| + 2, g(x) = 4x^2 + 1x - 5, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 0 |
math_algebra_func_area_level_1_1_1 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(3π(3x - 2) + 2) + 1, g(x) = -2x^2 + 2x + 4, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 1 |
math_algebra_func_area_level_1_1_2 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1e^(-1x) - 2) - 1)/(-3(-1e^(-1x) - 2) - 3) and g(x) = -3|x + 1| + 3 between the vertical lines x = -2.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6.5 | math | train | 2 |
math_algebra_func_area_level_1_1_3 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2(-4x^2 - 5x + 5) - 1 and g(x) = -2x - 4 from x = -2.0 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18.4 | math | train | 3 |
math_algebra_func_area_level_1_1_4 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-1cos(1πx - 2) + 1) + 5, g(x) = 2|x + 2| - 1, x = -4.1, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.7 | math | train | 4 |
math_algebra_func_area_level_1_1_5 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4x^2 + 1x) - 3 and g(x) = -4x^2 - 5x - 4 between the vertical lines x = -0.2 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | math | train | 5 |
math_algebra_func_area_level_1_1_6 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(3sin(1πx + 3) + 1) - 2)/(-2(3sin(1πx + 3) + 1) + 3) and g(x) = 1|x + 2| - 1 between the vertical lines x = 3.1 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10.6 | math | train | 6 |
math_algebra_func_area_level_1_1_7 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-2cos(3πx - 2) + 2) + 4, g(x) = -2x + 2, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.4 | math | train | 7 |
math_algebra_func_area_level_1_1_8 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(-2|x - 1|) - 2) - 1 and g(x) = (-2x + 3)/(-3x) between the vertical lines x = 4.4 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 8 |
math_algebra_func_area_level_1_1_9 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π(-3|x - 3| + 3)), g(x) = (-2x + 3)/(-2x - 2), x = 2.4, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 9 |
math_algebra_func_area_level_1_1_10 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(1π(1|x + 3| + 2)) - 3 and g(x) = 4x^2 + 4x - 5 from x = -1.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.9 | math | train | 10 |
math_algebra_func_area_level_1_1_11 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((-2x + 2)/(2x - 1)) + 1| and g(x) = 2|x - 2| - 1 from x = 1.9 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 11 |
math_algebra_func_area_level_1_1_12 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4x^2 + 3x - 3) - 1)/(1(-4x^2 + 3x - 3) - 2) and g(x) = -2|x - 2| + 2 between the vertical lines x = 0.8 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | math | train | 12 |
math_algebra_func_area_level_1_1_13 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(3π(-3x^2 + 1) + 3) + 2, g(x) = -1x - 3, x = -2.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 13 |
math_algebra_func_area_level_1_1_14 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1π((2x - 2)/(1x)) + 3) - 1 and g(x) = 5x + 3 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 14 |
math_algebra_func_area_level_1_1_15 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(3π(-1x^2 - 5x + 1) + 3) + 1 and g(x) = 1x - 4 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 15 |
math_algebra_func_area_level_1_1_16 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1x^2 + 3x - 1)^2 + 1(-1x^2 + 3x - 1), g(x) = -1x + 3, x = 0.0, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | math | train | 16 |
math_algebra_func_area_level_1_1_17 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = (1(5x^2 - 3x + 4) - 1)/(-2(5x^2 - 3x + 4) - 1) and g(x) = -2x^2 + 1x + 4 from x = -1.3 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9.0 | math | train | 17 |
math_algebra_func_area_level_1_1_18 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (3((2x - 2)/(1x)) + 3)/(2((2x - 2)/(1x)) - 1), g(x) = (-1x + 1)/(2x + 2), x = -0.6, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | math | train | 18 |
math_algebra_func_area_level_1_1_19 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-1x - 2)/(2x + 2)) - 3| + 3 and g(x) = 1x - 2 between the vertical lines x = -1.4 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | math | train | 19 |
math_algebra_func_area_level_1_1_20 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (1(1|x - 3| + 2))/(3(1|x - 3| + 2) + 1), g(x) = -3x^2 + 2x + 2, x = -0.5, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | math | train | 20 |
math_algebra_func_area_level_1_1_21 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1((1x + 2)/(2x + 3)) - 3 and g(x) = -3x^2 + 4x + 3 from x = -1.5 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.3 | math | train | 21 |
math_algebra_func_area_level_1_1_22 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(2πx - 2) - 3)^2 + 1(-2sin(2πx - 2) - 3) and g(x) = 2x from x = -3.7 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.3 | math | train | 22 |
math_algebra_func_area_level_1_1_23 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-1x^2 - 4x + 2)^2 + 3(-1x^2 - 4x + 2) - 5, g(x) = -2|x - 2| - 3, x = 0.2, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 23 |
math_algebra_func_area_level_1_1_24 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(1π(-5x + 4) - 2) and g(x) = 1|x + 2| from x = -2.1 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 24 |
math_algebra_func_area_level_1_1_25 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(1πx) + 3) + 2 and g(x) = 1x between the vertical lines x = -0.2 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 25 |
math_algebra_func_area_level_1_1_26 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2(3x^2 - 2x - 4)^2 + 1(3x^2 - 2x - 4) + 2 and g(x) = (2x)/(2x + 2) from x = 1.4 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 26 |
math_algebra_func_area_level_1_1_27 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(2πx + 2) - 2) + 5 and g(x) = 2x^2 + 3x + 3 from x = -2.3 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.3 | math | train | 27 |
math_algebra_func_area_level_1_1_28 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(2π(-1x^2 - 5x + 3) - 3) - 3, g(x) = -3x^2 + 5x + 2, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 28 |
math_algebra_func_area_level_1_1_29 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -5(2|x + 1| - 2) - 1 and g(x) = -4x - 4 from x = -1.6 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9.6 | math | train | 29 |
math_algebra_func_area_level_1_1_30 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-3x - 3)) - 1 and g(x) = (-2x - 3)/(1x + 3) between the vertical lines x = -0.6 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 30 |
math_algebra_func_area_level_1_1_31 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π(3x - 2) - 1) + 3 and g(x) = -4x - 5 from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | math | train | 31 |
math_algebra_func_area_level_1_1_32 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-4x^2 + 2x - 1) - 1 and g(x) = 2x - 4 from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.9 | math | train | 32 |
math_algebra_func_area_level_1_1_33 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(3πx) - 1)^2 + 4(1sin(3πx) - 1) + 1 and g(x) = -4x^2 + 2x from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.0 | math | train | 33 |
math_algebra_func_area_level_1_1_34 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(-3x^2 + 1)| - 1 and g(x) = 3x^2 - 5x + 2 from x = -2.4 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.4 | math | train | 34 |
math_algebra_func_area_level_1_1_35 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 2(1cos(3πx - 1)) + 2 and g(x) = 2x + 3 from x = -0.8 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | math | train | 35 |
math_algebra_func_area_level_1_1_36 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1(-2x^2 + 5x + 5)) + 2 and g(x) = -2|x - 3| + 2 from x = -1.0 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15.1 | math | train | 36 |
math_algebra_func_area_level_1_1_37 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-1sin(3πx - 1) + 2)| + 3, g(x) = -2x + 1, x = -1.9, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 37 |
math_algebra_func_area_level_1_1_38 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(3π(-1x^2 + 3x - 4) + 2) + 2, g(x) = (1x)/(3x + 2), x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 38 |
math_algebra_func_area_level_1_1_39 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(3π(4x + 3) - 2) + 2, g(x) = 5x^2 + 2x - 1, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 39 |
math_algebra_func_area_level_1_1_40 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(-1x + 2) - 2) + 1 and g(x) = (2x - 1)/(2x + 2) between the vertical lines x = 2.4 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | math | train | 40 |
math_algebra_func_area_level_1_1_41 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 2cos(3π(2|x + 2| + 2) - 3) - 3, g(x) = -2x - 3, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 41 |
math_algebra_func_area_level_1_1_42 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-2x - 1)/(-3x - 2)) + 3 and g(x) = 2|x + 3| from x = -1.0 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 42 |
math_algebra_func_area_level_1_1_43 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1cos(2π(4x^2 - 5x + 5)) + 2 and g(x) = -5x + 2 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 43 |
math_algebra_func_area_level_1_1_44 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-3cos(1πx - 1) + 1) + 3| - 2 and g(x) = 4x + 5 from x = -4.3 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | math | train | 44 |
math_algebra_func_area_level_1_1_45 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(3cos(2πx)) + 3| - 1, g(x) = 1x^2 - 3, x = 2.3, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | math | train | 45 |
math_algebra_func_area_level_1_1_46 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(1x - 4) - 1) + 3 and g(x) = (1x - 3)/(1x + 1) between the vertical lines x = -3.2 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | math | train | 46 |
math_algebra_func_area_level_1_1_47 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (3(3cos(3πx + 3)) + 2)/(-3(3cos(3πx + 3)) - 1), g(x) = -1|x + 3| + 1, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | math | train | 47 |
math_algebra_func_area_level_1_1_48 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -1((1x + 2)/(3x + 2))^2 - 5((1x + 2)/(3x + 2)) - 3, g(x) = -1x, x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 48 |
math_algebra_func_area_level_1_1_49 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -5(-3sin(1πx + 2) + 2) - 4 and g(x) = (2x)/(-1x - 2) from x = 1.7 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | math | train | 49 |
math_algebra_func_area_level_1_1_50 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -3(-5x^2 + 2x + 1)^2 - 3(-5x^2 + 2x + 1) + 1, g(x) = (1x + 1)/(3x + 2), x = -0.3, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.1 | math | train | 50 |
math_algebra_func_area_level_1_1_51 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -4(1x^2 - 5x + 2)^2 + 4 and g(x) = 1|x| + 2 from x = 0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 51 |
math_algebra_func_area_level_1_1_52 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1x - 1) and g(x) = -4x^2 + 3x + 5 between the vertical lines x = -0.6 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.5 | math | train | 52 |
math_algebra_func_area_level_1_1_53 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(2cos(3πx + 3) - 2) - 3)/(-2(2cos(3πx + 3) - 2) - 1), g(x) = (-2x + 1)/(-2x + 3), x = 1.1, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44.5 | math | train | 53 |
math_algebra_func_area_level_1_1_54 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3sin(2πx + 2) - 3) + 2)/(-2(-3sin(2πx + 2) - 3) - 3) and g(x) = 2|x| between the vertical lines x = 3.3 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.8 | math | train | 54 |
math_algebra_func_area_level_1_1_55 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1x + 2)/(-3x - 1))^2 + 1((1x + 2)/(-3x - 1)) + 5 and g(x) = 3|x + 2| + 2 between the vertical lines x = -3.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2.1 | math | train | 55 |
math_algebra_func_area_level_1_1_56 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = (3(2x^2 + 4x - 1) + 2)/(3(2x^2 + 4x - 1)) and g(x) = 3x - 2 from x = 0.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.5 | math | train | 56 |
math_algebra_func_area_level_1_1_57 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(1cos(2πx + 1) + 1) + 3)/(-2(1cos(2πx + 1) + 1) + 3) and g(x) = -1x - 5 from x = 4.0 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.7 | math | train | 57 |
math_algebra_func_area_level_1_1_58 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2e^(1(-1|x + 3| + 3)) + 1 and g(x) = 3|x| - 3 from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | math | train | 58 |
math_algebra_func_area_level_1_1_59 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (1(1x^2 - 5x + 1) - 1)/(-2(1x^2 - 5x + 1)), g(x) = -1|x + 2| - 3, x = 0.2, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32.3 | math | train | 59 |
math_algebra_func_area_level_1_1_60 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(-3x^2 + 3x + 4) - 3) + 3, g(x) = -2x - 1, x = -2.4, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 60 |
math_algebra_func_area_level_1_1_61 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(1πx + 3)) + 1)/(-3(-3cos(1πx + 3)) + 2) and g(x) = -3x^2 - 1x + 1 between the vertical lines x = -3.5 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24.8 | math | train | 61 |
math_algebra_func_area_level_1_1_62 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3cos(3πx) - 1) + 2)/(-3(-3cos(3πx) - 1) - 1) and g(x) = -1x^2 + 5x + 5 between the vertical lines x = -2.5 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.1 | math | train | 62 |
math_algebra_func_area_level_1_1_63 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-1x - 5) + 2)/(-2(-1x - 5) - 1) and g(x) = 3|x - 3| - 3 from x = 2.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | math | train | 63 |
math_algebra_func_area_level_1_1_64 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = (2(2cos(2πx - 1) - 2) - 1)/(3(2cos(2πx - 1) - 2) + 1) and g(x) = -4x + 1 from x = -3.9 to x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | math | train | 64 |
math_algebra_func_area_level_1_1_65 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-3x + 2)/(3x - 1))| - 1 and g(x) = -3|x - 2| + 2 from x = 1.2 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | math | train | 65 |
math_algebra_func_area_level_1_1_66 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π((3x + 1)/(2x + 3)) - 3) - 2, g(x) = (-1x)/(1x - 3), x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 66 |
math_algebra_func_area_level_1_1_67 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-4x^2 + 3x + 3) - 1)/(3(-4x^2 + 3x + 3) - 2), g(x) = 3|x + 1| + 1, x = -0.5, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13.5 | math | train | 67 |
math_algebra_func_area_level_1_1_68 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(3π(2x^2 - 5x) - 1) and g(x) = 4x^2 - 4x - 4 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 68 |
math_algebra_func_area_level_1_1_69 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(1|x - 2| - 1) + 3)/(3(1|x - 2| - 1) + 2), g(x) = -1|x| - 3, x = 1.9, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 69 |
math_algebra_func_area_level_1_1_70 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2(2x + 2) and g(x) = (-1x + 3)/(2x - 1) from x = -0.6 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | math | train | 70 |
math_algebra_func_area_level_1_1_71 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1π(-1x^2 + 1)) - 3 and g(x) = 1x - 4 between the vertical lines x = 2.0 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 71 |
math_algebra_func_area_level_1_1_72 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1cos(2πx + 1) + 3) - 1| and g(x) = 2x^2 - 5x between the vertical lines x = -0.4 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.2 | math | train | 72 |
math_algebra_func_area_level_1_1_73 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(3πx + 3) + 2) - 3)/(1(3cos(3πx + 3) + 2)), g(x) = (2x + 3)/(3x + 1), x = 2.2, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | math | train | 73 |
math_algebra_func_area_level_1_1_74 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(2πx - 2)) + 1 and g(x) = -5x^2 - 3x + 3 between the vertical lines x = -1.1 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.9 | math | train | 74 |
math_algebra_func_area_level_1_1_75 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3x^2 + 1x) + 2 and g(x) = 3x between the vertical lines x = -0.9 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.3 | math | train | 75 |
math_algebra_func_area_level_1_1_76 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-2x^2 - 1x + 3) - 2 and g(x) = -1x^2 - 2x + 2 from x = -2.1 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16.6 | math | train | 76 |
math_algebra_func_area_level_1_1_77 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 1cos(3π(-1x^2 - 4x)) - 2 and g(x) = (3x + 1)/(-1x + 2) from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | math | train | 77 |
math_algebra_func_area_level_1_1_78 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-1cos(3πx - 3) + 3) + 2)/(1(-1cos(3πx - 3) + 3) - 2), g(x) = -3x + 1, x = 2.5, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | math | train | 78 |
math_algebra_func_area_level_1_1_79 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-2|x - 2| + 3) - 3)/(-3(-2|x - 2| + 3) - 1), g(x) = 1x + 2, x = 0.5, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9.1 | math | train | 79 |
math_algebra_func_area_level_1_1_80 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -1((-2x - 2)/(-2x)) - 5 and g(x) = 1x - 2 from x = -3.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.3 | math | train | 80 |
math_algebra_func_area_level_1_1_81 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-2cos(2πx + 2) + 1) + 3)/(-1(-2cos(2πx + 2) + 1) + 2), g(x) = 5x^2 - 1x, x = -1.6, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.1 | math | train | 81 |
math_algebra_func_area_level_1_1_82 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(2x + 4) + 2) + 1 and g(x) = 3x^2 + 5x - 2 between the vertical lines x = -2.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.8 | math | train | 82 |
math_algebra_func_area_level_1_1_83 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(3πx - 2) + 2) + 2 and g(x) = 3x + 2 from x = -1.1 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.1 | math | train | 83 |
math_algebra_func_area_level_1_1_84 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2e^(2x)) + 3)/(-1(-2e^(2x)) + 2) and g(x) = (1x + 3)/(-3x + 2) between the vertical lines x = -0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22.5 | math | train | 84 |
math_algebra_func_area_level_1_1_85 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-1sin(3πx - 3) + 1)^2 - 4(-1sin(3πx - 3) + 1) + 2, g(x) = -1x + 1, x = 0.6, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6.7 | math | train | 85 |
math_algebra_func_area_level_1_1_86 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2|x| - 1) - 1)/(-2(-2|x| - 1) + 3) and g(x) = -3|x - 3| + 2 between the vertical lines x = 2.6 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | math | train | 86 |
math_algebra_func_area_level_1_1_87 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(2π(-4x^2 - 4x + 4) + 1) + 2 and g(x) = -2x - 5 from x = -3.1 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 87 |
math_algebra_func_area_level_1_1_88 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1(3|x - 3| + 3)) + 1, g(x) = -2x^2 + 4x, x = 0.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | math | train | 88 |
math_algebra_func_area_level_1_1_89 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2((3x + 1)/(-1x + 3)) - 1 and g(x) = 3|x| - 3 from x = -1.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | math | train | 89 |
math_algebra_func_area_level_1_1_90 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(3π(-1x - 2) - 3), g(x) = -4x + 3, x = 0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 90 |
math_algebra_func_area_level_1_1_91 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(2π(2|x + 3| + 2) - 2) + 2 and g(x) = 1x - 2 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | math | train | 91 |
math_algebra_func_area_level_1_1_92 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = (-3((-2x - 1)/(-1x)) + 1)/(3((-2x - 1)/(-1x)) - 2) and g(x) = (-3x - 1)/(1x + 1) from x = -0.7 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | math | train | 92 |
math_algebra_func_area_level_1_1_93 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = -2(-2sin(2πx + 1) + 3)^2 + 2(-2sin(2πx + 1) + 3) + 3 and g(x) = -1x^2 + 2x + 5 from x = 3.9 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.9 | math | train | 93 |
math_algebra_func_area_level_1_1_94 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|x - 3| - 1)^2 - 3(2|x - 3| - 1) + 3 and g(x) = -3x + 3 between the vertical lines x = 2.0 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17.0 | math | train | 94 |
math_algebra_func_area_level_1_1_95 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(3π(-5x^2 + 1x - 3) - 2) - 3 and g(x) = -5x^2 - 2x + 3 from x = 0.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 95 |
math_algebra_func_area_level_1_1_96 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2e^(1x) - 3) - 1| + 1 and g(x) = -5x^2 - 5x + 3 between the vertical lines x = 0.5 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.2 | math | train | 96 |
math_algebra_func_area_level_1_1_97 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3e^(1x) + 3) - 4 and g(x) = 1x + 2 between the vertical lines x = -2.8 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | math | train | 97 |
math_algebra_func_area_level_1_1_98 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(1π(2|x - 3| + 2) - 3), g(x) = 1x + 3, x = -1.3, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | math | train | 98 |
math_algebra_func_area_level_1_1_99 | algebra_func_area1 | easy (level 1) | 1 | [
{
"content": "Calculate the area enclosed between the functions f(x) = 3((3x + 2)/(2x - 3))^2 - 5 and g(x) = (-1x + 3)/(-3x - 1) from x = -0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | math | train | 99 |
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