id
string | setting_key
string | difficulty
string | level
int64 | messages
list | ground_truth
string | dataset
string | omega_split
string | __index_level_0__
int64 |
|---|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_2_2_400
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1e^(2((-2x + 1)/(1x - 3))) + 1) - 1)/(-1(-1e^(2((-2x + 1)/(1x - 3))) + 1) - 1) and g(x) = -2sin(1π(2|x - 3| + 3) + 3) + 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"
}
] |
1.3
|
math
|
train
| 160,465 |
math_algebra_func_area_level_2_2_401
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(4(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) + 4))/(-1(4(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) + 4)), g(x) = 3sin(1π(-1x^2 + 3x + 4) - 1), x = -2.0, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,466 |
math_algebra_func_area_level_2_2_402
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(1π(-3x + 5) + 2)) + 5 and g(x) = 2|(3x + 4) - 2| + 2 from x = 0.4 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.1
|
math
|
train
| 160,467 |
math_algebra_func_area_level_2_2_403
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((2((-3x - 2)/(-1x - 1)) + 2)/(3((-3x - 2)/(-1x - 1)) + 1)) - 2, g(x) = 1(-3cos(2πx + 3) - 3) - 1, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,468 |
math_algebra_func_area_level_2_2_404
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(3|(3x + 4) - 1| + 1)^2 - 2(3|(3x + 4) - 1| + 1) - 4 and g(x) = -3((1x + 2)/(1x + 1))^2 - 1((1x + 2)/(1x + 1)) from x = -1.2 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-36.8
|
math
|
train
| 160,469 |
math_algebra_func_area_level_2_2_405
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-1(-3e^(-1x) + 3)^2 - 2(-3e^(-1x) + 3) - 2) - 2, g(x) = -1((3x + 1)/(-1x + 2)) + 1, x = -0.5, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,470 |
math_algebra_func_area_level_2_2_406
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(1π(2|(3x + 2) - 3| - 3) + 1) - 2, g(x) = -1e^(-1(5x^2 + 5x - 2)), x = -1.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17.1
|
math
|
train
| 160,471 |
math_algebra_func_area_level_2_2_407
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(2π((3(-3|x - 3| + 1) + 1)/(1(-3|x - 3| + 1))) + 1) + 3, g(x) = (3(-3|x + 2| - 2) - 3)/(3(-3|x + 2| - 2) - 2), x = 3.3, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,472 |
math_algebra_func_area_level_2_2_408
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(-3((-1x + 3)/(-3x + 1)) + 1) + 2| + 3, g(x) = -1sin(2π((-3x - 2)/(1x)) - 3) - 3, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,473 |
math_algebra_func_area_level_2_2_409
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((2((2x - 3)/(3x - 1)) - 3)/(3((2x - 3)/(3x - 1)) + 3)) - 2)/(2((2((2x - 3)/(3x - 1)) - 3)/(3((2x - 3)/(3x - 1)) + 3))), g(x) = (-3(3x - 4) + 2)/(-2(3x - 4)), x = 1.8, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,474 |
math_algebra_func_area_level_2_2_410
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-3sin(1π(1x^2 + 1x + 4)) - 2)^2 + 2(-3sin(1π(1x^2 + 1x + 4)) - 2) - 4, g(x) = -2(-4x - 3)^2 - 1(-4x - 3), x = -0.9, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.6
|
math
|
train
| 160,475 |
math_algebra_func_area_level_2_2_411
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((2(1x^2 + 4x - 4))/(3(1x^2 + 4x - 4) + 1)) + 2| + 1 and g(x) = -2(-1e^(-2x) - 3) - 1 between the vertical lines x = 0.2 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
math
|
train
| 160,476 |
math_algebra_func_area_level_2_2_412
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|(-1x - 2)| - 3) - 2)/(2(-1|(-1x - 2)| - 3) - 1), g(x) = 2sin(3π(2|x + 1|) - 3) + 1, x = 3.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,477 |
math_algebra_func_area_level_2_2_413
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(4(3|x + 1| - 1)^2 - 3(3|x + 1| - 1) - 5)| - 1 and g(x) = (1(3cos(3πx + 1) + 3) + 3)/(1(3cos(3πx + 1) + 3) + 2) between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,478 |
math_algebra_func_area_level_2_2_414
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3π(4(-3x^2 + 1x + 1)^2 + 3(-3x^2 + 1x + 1) - 5)) - 2 and g(x) = -1|(2|x + 3| + 2) - 2| - 2 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,479 |
math_algebra_func_area_level_2_2_415
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-1e^(-1((-1x + 2)/(2x + 1))) + 1) + 2)/(1(-1e^(-1((-1x + 2)/(2x + 1))) + 1) + 3) and g(x) = -3cos(1π(-1|x| + 2) + 2) + 1 from x = 1.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
math
|
train
| 160,480 |
math_algebra_func_area_level_2_2_416
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2((-1((-3x - 3)/(3x + 3)) - 3)/(-3((-3x - 3)/(3x + 3)) + 2)) + 4 and g(x) = 1|(-5x^2 - 4x + 1) + 3| + 1 from x = 0.0 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.6
|
math
|
train
| 160,481 |
math_algebra_func_area_level_2_2_417
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(3cos(1π(-1x^2 + 2x + 1) + 3) + 2) - 2, g(x) = -1(2|x + 2| - 3)^2 + 5(2|x + 2| - 3) - 1, x = -4.2, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 160,482 |
math_algebra_func_area_level_2_2_418
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(4(-2|x + 2| + 1) - 4)^2 - 5(4(-2|x + 2| + 1) - 4) + 1, g(x) = -2|(-2x - 2)| - 2, x = -2.8, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.2
|
math
|
train
| 160,483 |
math_algebra_func_area_level_2_2_419
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(1(-2x) - 4) + 3, g(x) = 2cos(1π(-2|x - 3| - 2) - 3) + 1, x = -1.7, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 160,484 |
math_algebra_func_area_level_2_2_420
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(1e^(-2(1x + 2)) - 2) - 2| + 1, g(x) = 2sin(1π(-3|x - 3| - 2)) + 3, x = -2.9, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,485 |
math_algebra_func_area_level_2_2_421
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3((2(-2cos(3πx + 1) - 1) + 3)/(2(-2cos(3πx + 1) - 1) - 1)))/(3((2(-2cos(3πx + 1) - 1) + 3)/(2(-2cos(3πx + 1) - 1) - 1)) + 3) and g(x) = -2e^(2(-4x + 3)) + 2 from x = 2.1 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 160,486 |
math_algebra_func_area_level_2_2_422
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3π((3(2|x + 3|) + 2)/(1(2|x + 3|) + 1))) and g(x) = 2(2cos(1πx) + 3) - 2 between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,487 |
math_algebra_func_area_level_2_2_423
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2sin(1π((-1x - 3)/(2x + 3)) - 2) + 2)^2 + 5(-2sin(1π((-1x - 3)/(2x + 3)) - 2) + 2) - 3 and g(x) = -4(-3cos(2πx + 1))^2 + 5(-3cos(2πx + 1)) - 1 between the vertical lines x = 1.1 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,488 |
math_algebra_func_area_level_2_2_424
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(5(-1x^2 + 4x - 2)^2 + 3(-1x^2 + 4x - 2) + 1) + 2) + 2 and g(x) = 4(5x^2 - 3x - 1) between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,489 |
math_algebra_func_area_level_2_2_425
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1sin(3π((-2x + 3)/(2x + 1)) + 1) - 3) + 2)/(2(-1sin(3π((-2x + 3)/(2x + 1)) + 1) - 3) + 3) and g(x) = 3cos(2π(-1x^2 - 5x + 5) + 3) between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,490 |
math_algebra_func_area_level_2_2_426
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-4((1x - 3)/(-3x + 2))^2 - 3((1x - 3)/(-3x + 2)) - 1) + 2| + 3, g(x) = 3(-1|x + 1| - 2)^2 + 1(-1|x + 1| - 2) + 2, x = 0.4, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-34.8
|
math
|
train
| 160,491 |
math_algebra_func_area_level_2_2_427
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(-3(-2cos(3πx - 2) + 2) + 5) + 4 and g(x) = -2(3|x - 3| - 2)^2 + 3(3|x - 3| - 2) + 4 from x = 1.3 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.4
|
math
|
train
| 160,492 |
math_algebra_func_area_level_2_2_428
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-2((-3x + 2)/(2x - 1)) + 1)/(3((-3x + 2)/(2x - 1)) - 1))^2 - 3((-2((-3x + 2)/(2x - 1)) + 1)/(3((-3x + 2)/(2x - 1)) - 1)) and g(x) = 2|((1x - 2)/(-1x + 3)) + 2| - 1 between the vertical lines x = 2.1 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89.8
|
math
|
train
| 160,493 |
math_algebra_func_area_level_2_2_429
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-3cos(1π(1x^2 + 2x + 3) + 3))^2 - 5 and g(x) = 3|(3e^(-1x) + 2) - 2| + 3 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 160,494 |
math_algebra_func_area_level_2_2_430
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1(-2|x + 1| + 1)^2 + 1(-2|x + 1| + 1) - 5) - 3| + 3 and g(x) = -1(1|x| - 1)^2 - 3(1|x| - 1) - 3 between the vertical lines x = 0.6 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.0
|
math
|
train
| 160,495 |
math_algebra_func_area_level_2_2_431
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(3(-3x - 2) + 2) + 3| + 1 and g(x) = 2(1cos(3πx - 3) + 2)^2 - 3(1cos(3πx - 3) + 2) - 3 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"
}
] |
1.5
|
math
|
train
| 160,496 |
math_algebra_func_area_level_2_2_432
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1sin(3π(-2|x + 2| + 1) - 2) + 2) + 3| + 2 and g(x) = -3|(5x + 4) - 2| - 1 between the vertical lines x = -0.5 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,497 |
math_algebra_func_area_level_2_2_433
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2sin(1π(2x - 4) - 1) - 2)^2 + 4(-2sin(1π(2x - 4) - 1) - 2) + 2 and g(x) = 3|(-2|x| + 2) + 1| - 2 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,498 |
math_algebra_func_area_level_2_2_434
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(2sin(1π(-5x + 4) - 2) + 2)| - 3, g(x) = -3(-3sin(3πx - 2) + 2) - 4, x = -1.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18.2
|
math
|
train
| 160,499 |
math_algebra_func_area_level_2_2_435
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-4(2e^(-1x) - 3) + 4)^2 - 4(-4(2e^(-1x) - 3) + 4) - 4, g(x) = (-3(-3cos(1πx - 2) - 3) + 1)/(2(-3cos(1πx - 2) - 3) - 3), x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,500 |
math_algebra_func_area_level_2_2_436
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2|((-2x - 2)/(1x + 2)) + 2| - 3) - 1| - 2 and g(x) = 5(-1x^2 + 3x - 5) - 3 between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
81.3
|
math
|
train
| 160,501 |
math_algebra_func_area_level_2_2_437
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-3((-2x + 3)/(3x - 1)) - 4) + 1| - 3 and g(x) = -1|(-1x^2 + 4x + 5) + 2| - 2 from x = 1.4 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7.0
|
math
|
train
| 160,502 |
math_algebra_func_area_level_2_2_438
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(3sin(3π(1x^2 + 1x - 4) + 2) + 2)^2 - 2(3sin(3π(1x^2 + 1x - 4) + 2) + 2) + 5, g(x) = (-2(3|x - 2| + 1) + 3)/(-3(3|x - 2| + 1) - 2), x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.6
|
math
|
train
| 160,503 |
math_algebra_func_area_level_2_2_439
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(1π(1(1x^2 + 3x) - 1) - 2) + 3 and g(x) = -2cos(2π((2x + 3)/(-2x - 3)) - 3) from x = -3.6 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 160,504 |
math_algebra_func_area_level_2_2_440
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-5(-2sin(1πx - 3) + 1)^2 - 4(-2sin(1πx - 3) + 1) + 3) - 3)/(-2(-5(-2sin(1πx - 3) + 1)^2 - 4(-2sin(1πx - 3) + 1) + 3) - 3) and g(x) = -3|((-3x)/(1x + 3))| - 2 between the vertical lines x = 1.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.4
|
math
|
train
| 160,505 |
math_algebra_func_area_level_2_2_441
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1((1x + 3)/(1x + 2))^2 + 1((1x + 3)/(1x + 2)) + 1)^2 - 1(1((1x + 3)/(1x + 2))^2 + 1((1x + 3)/(1x + 2)) + 1) + 2 and g(x) = -2sin(3π(1|x + 3| - 1) + 3) + 3 between the vertical lines x = -2.6 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,506 |
math_algebra_func_area_level_2_2_442
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((3((-1x + 2)/(1x - 3)) - 3)/(3((-1x + 2)/(1x - 3)) - 2)) + 2 and g(x) = (2((-3x - 1)/(-3x - 3)) + 2)/(-1((-3x - 1)/(-3x - 3)) + 2) between the vertical lines x = -1.2 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28.6
|
math
|
train
| 160,507 |
math_algebra_func_area_level_2_2_443
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-2(1e^(-2x) - 1)^2 + 5(1e^(-2x) - 1) - 4) + 3)/(-2(-2(1e^(-2x) - 1)^2 + 5(1e^(-2x) - 1) - 4) - 3) and g(x) = 5(4x - 1) + 4 from x = -0.3 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.4
|
math
|
train
| 160,508 |
math_algebra_func_area_level_2_2_444
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-2|((2x + 1)/(-1x - 2)) - 3| - 2) - 3, g(x) = 4(1e^(2x) - 3) + 2, x = -1.6, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
train
| 160,509 |
math_algebra_func_area_level_2_2_445
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(-3|((1x - 2)/(-3x + 4)) + 1| + 1) + 1 and g(x) = -3(-2|x - 3| + 3)^2 - 2(-2|x - 3| + 3) + 1 from x = 0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,510 |
math_algebra_func_area_level_2_2_446
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(1|(-3x + 3) - 3| - 2) + 5 and g(x) = 2((2x + 1)/(2x + 3)) + 5 from x = -1.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
81.1
|
math
|
train
| 160,511 |
math_algebra_func_area_level_2_2_447
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(1|(3|x - 1|) - 1| - 3) - 1| + 3, g(x) = 4(-3sin(1πx + 3) - 3)^2 - 2(-3sin(1πx + 3) - 3), x = 2.4, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 160,512 |
math_algebra_func_area_level_2_2_448
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-2|((2x - 3)/(3x + 1)) - 2| - 1) - 1| + 1 and g(x) = 3e^(2(1x + 2)) - 2 from x = -1.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23.2
|
math
|
train
| 160,513 |
math_algebra_func_area_level_2_2_449
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3|(1cos(1πx + 3) - 2) + 1| + 1) + 1 and g(x) = 4(3x + 1) + 5 between the vertical lines x = -2.2 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.6
|
math
|
train
| 160,514 |
math_algebra_func_area_level_2_2_450
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3((2(-1|x + 2|) + 2)/(-2(-1|x + 2|) - 3)) + 4, g(x) = -2|(-1x + 1) + 3| - 3, x = -3.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
81.9
|
math
|
train
| 160,515 |
math_algebra_func_area_level_2_2_451
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3π((3((2x - 3)/(-3x - 1)) + 1)/(3((2x - 3)/(-3x - 1)) - 1)) + 2) and g(x) = 1sin(3π(-4x + 2)) between the vertical lines x = 3.3 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,516 |
math_algebra_func_area_level_2_2_452
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π(1(4x + 4) - 5)) - 2 and g(x) = 1(-3x + 5) - 4 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,517 |
math_algebra_func_area_level_2_2_453
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3π((3((1x - 1)/(-2x + 3)))/(-1((1x - 1)/(-2x + 3)) - 2)) + 1) + 2 and g(x) = 5(2x^2 + 3x)^2 - 3(2x^2 + 3x) between the vertical lines x = -1.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.7
|
math
|
train
| 160,518 |
math_algebra_func_area_level_2_2_454
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((2(3|x + 2| - 2) - 1)/(2(3|x + 2| - 2) + 2)) + 2)/(-2((2(3|x + 2| - 2) - 1)/(2(3|x + 2| - 2) + 2))) and g(x) = -1sin(1π((3x + 3)/(1x + 1))) - 1 between the vertical lines x = -2.3 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,519 |
math_algebra_func_area_level_2_2_455
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((2(-2sin(1πx - 1) - 1) + 2)/(-2(-2sin(1πx - 1) - 1) - 3))^2 + 4((2(-2sin(1πx - 1) - 1) + 2)/(-2(-2sin(1πx - 1) - 1) - 3)) - 2, g(x) = -2(-1x + 4)^2 - 2, x = 3.3, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.0
|
math
|
train
| 160,520 |
math_algebra_func_area_level_2_2_456
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(3|x - 1| - 2)) - 3)/(-1(3(3|x - 1| - 2))) and g(x) = -3(-2sin(3πx + 1) - 3)^2 + 3(-2sin(3πx + 1) - 3) + 2 between the vertical lines x = 0.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48.3
|
math
|
train
| 160,521 |
math_algebra_func_area_level_2_2_457
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2((1(4x + 3) + 3)/(-2(4x + 3) + 3)) + 1)/(-3((1(4x + 3) + 3)/(-2(4x + 3) + 3)) - 1) and g(x) = 2((1x + 2)/(-2x + 3)) - 4 from x = -3.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.6
|
math
|
train
| 160,522 |
math_algebra_func_area_level_2_2_458
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(3π(-5x - 4) + 1) + 1))/(2(3cos(3π(-5x - 4) + 1) + 1) - 1), g(x) = -2cos(3π((-2x + 3)/(1x + 2))) - 2, x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 160,523 |
math_algebra_func_area_level_2_2_459
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1e^(2(1|(-4x^2 + 5x + 5)| - 3)) - 2, g(x) = -2e^(-1(4x + 3)) - 2, x = -1.0, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 160,524 |
math_algebra_func_area_level_2_2_460
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1e^(2((-1((3x + 3)/(-1x - 3)) + 3)/(3((3x + 3)/(-1x - 3)) - 1))), g(x) = 2|(-1x^2 - 5x + 1)| - 1, x = 0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,525 |
math_algebra_func_area_level_2_2_461
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4(-1e^(-2x) + 2) - 2) - 3)/(3(-4(-1e^(-2x) + 2) - 2)) and g(x) = -1(1x^2 + 4x + 4)^2 + 4(1x^2 + 4x + 4) + 2 between the vertical lines x = -4.1 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17.0
|
math
|
train
| 160,526 |
math_algebra_func_area_level_2_2_462
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2cos(2π(1x^2 + 1x + 3) + 1) - 2) + 3 and g(x) = (1(2|x - 3| - 3) - 2)/(1(2|x - 3| - 3)) between the vertical lines x = 3.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,527 |
math_algebra_func_area_level_2_2_463
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-5(3cos(3πx - 3) - 1)) + 1)/(-1(-5(3cos(3πx - 3) - 1)) - 1), g(x) = 1|((1x)/(-2x + 3)) + 2| - 2, x = -4.9, and x = -4.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
math
|
train
| 160,528 |
math_algebra_func_area_level_2_2_464
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-1cos(1π((-2x + 2)/(-1x + 2)) - 2)) + 1 and g(x) = -1(2x^2 - 4x - 5) - 4 between the vertical lines x = 1.8 and x = 1.9000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,529 |
math_algebra_func_area_level_2_2_465
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-3|(2sin(2πx + 2)) - 2| + 2) - 2)/(2(-3|(2sin(2πx + 2)) - 2| + 2) - 3), g(x) = 2|(-2x^2 - 1) + 3| + 2, x = -2.0, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.9
|
math
|
train
| 160,530 |
math_algebra_func_area_level_2_2_466
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(2(-3sin(1πx - 3)) + 4) - 5 and g(x) = 3(3cos(3πx - 3) - 3) + 1 from x = 1.8 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40.1
|
math
|
train
| 160,531 |
math_algebra_func_area_level_2_2_467
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-1(2x + 3)^2 + 5(2x + 3) - 3) - 2)/(2(-1(2x + 3)^2 + 5(2x + 3) - 3) - 1) and g(x) = (-2((1x + 2)/(-1x + 3)) - 3)/(-3((1x + 2)/(-1x + 3))) from x = 0.7 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,532 |
math_algebra_func_area_level_2_2_468
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((2((-1x - 3)/(-2x - 2)) - 1)/(3((-1x - 3)/(-2x - 2)) - 2)) + 2 and g(x) = (-1(-1cos(1πx) - 2) - 3)/(1(-1cos(1πx) - 2) - 2) between the vertical lines x = -4.6 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,533 |
math_algebra_func_area_level_2_2_469
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(-3(1sin(2πx - 2) - 3) - 4)^2 + 1(-3(1sin(2πx - 2) - 3) - 4) + 1 and g(x) = -5(3|x + 2| + 1)^2 - 1(3|x + 2| + 1) + 5 from x = -3.2 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60.0
|
math
|
train
| 160,534 |
math_algebra_func_area_level_2_2_470
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-2(-5x)^2 + 2(-5x) + 3) - 3| + 2 and g(x) = 2(1sin(1πx + 1) + 1)^2 - 3(1sin(1πx + 1) + 1) + 3 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,535 |
math_algebra_func_area_level_2_2_471
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-2sin(1π((1x - 3)/(1x)) + 2) + 3)^2 + 4, g(x) = 4(1cos(2πx + 1) - 3) + 3, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.8
|
math
|
train
| 160,536 |
math_algebra_func_area_level_2_2_472
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3e^(-1(-1((1x - 3)/(-2x))^2 + 1((1x - 3)/(-2x)) + 4)) + 1 and g(x) = 3sin(2π(-1x^2 - 2x + 3) - 3) + 1 from x = 2.4 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,537 |
math_algebra_func_area_level_2_2_473
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2sin(1π((3x + 3)/(-2x - 3)) + 1) - 3) + 3 and g(x) = -5(1x + 2) + 1 between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,538 |
math_algebra_func_area_level_2_2_474
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1e^(-1(1|(-1x^2 - 1x + 5)| - 2)) + 3, g(x) = -1cos(1π((-2x - 3)/(-1x - 2)) + 3), x = 1.5, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 160,539 |
math_algebra_func_area_level_2_2_475
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-1(-1x^2 - 2x - 2) - 2) - 3)/(3(-1(-1x^2 - 2x - 2) - 2) + 2), g(x) = 3sin(3π(2|x - 3| - 1) + 1), x = 0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 160,540 |
math_algebra_func_area_level_2_2_476
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(4((3x - 1)/(2x + 2)) + 3))/(-2(4((3x - 1)/(2x + 2)) + 3) - 1) and g(x) = 1sin(3π(1x^2 - 5) - 3) + 1 between the vertical lines x = 1.8 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,541 |
math_algebra_func_area_level_2_2_477
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(5(-1sin(3πx)))^2 - 2(5(-1sin(3πx))) - 2, g(x) = 3|((-3x - 1)/(-3x + 2)) + 3| + 3, x = 0.9, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.4
|
math
|
train
| 160,542 |
math_algebra_func_area_level_2_2_478
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(-5x) - 2| + 1) - 3)/(-3(-1|(-5x) - 2| + 1) - 3), g(x) = -2cos(2π(-3x^2 - 4x - 1)) + 2, x = -0.7, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 160,543 |
math_algebra_func_area_level_2_2_479
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((2(3x^2 + 1x - 3) - 3)/(1(3x^2 + 1x - 3) + 2)) + 1)/(2((2(3x^2 + 1x - 3) - 3)/(1(3x^2 + 1x - 3) + 2)) + 2), g(x) = -1|(-1|x + 2| + 2) - 1| - 1, 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"
}
] |
1.6
|
math
|
train
| 160,544 |
math_algebra_func_area_level_2_2_480
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(1π(3(-2x^2 + 4x - 2) + 4) - 3) - 1, g(x) = (-2(-2x) - 2)/(-2(-2x)), x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,545 |
math_algebra_func_area_level_2_2_481
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2cos(2π(1((1x - 2)/(3x + 2))^2 + 4((1x - 2)/(3x + 2)) + 1) - 3) + 1, g(x) = 1(-4x - 3) + 2, 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"
}
] |
0.1
|
math
|
train
| 160,546 |
math_algebra_func_area_level_2_2_482
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1|((1x - 3)/(2x + 3)) + 1| - 2)^2 + 3(1|((1x - 3)/(2x + 3)) + 1| - 2) + 5 and g(x) = -5(-2x^2 - 4x - 3) - 3 between the vertical lines x = -1.0 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,547 |
math_algebra_func_area_level_2_2_483
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(2π(1|(2|x + 1| - 1) - 2|)) - 3 and g(x) = 2sin(2π(1x + 3) - 1) + 1 from x = 1.9 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,548 |
math_algebra_func_area_level_2_2_484
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|((-3(1|x| - 1))/(3(1|x| - 1) - 2))| + 2, g(x) = 1(-3cos(1πx) - 2)^2 - 2(-3cos(1πx) - 2) + 2, x = -1.7, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27.8
|
math
|
train
| 160,549 |
math_algebra_func_area_level_2_2_485
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(2|x + 3| - 2) - 4) + 1)/(-2(1(2|x + 3| - 2) - 4)) and g(x) = (-3(1x^2 - 1x - 2) + 3)/(-1(1x^2 - 1x - 2) + 2) between the vertical lines x = -0.2 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14.6
|
math
|
train
| 160,550 |
math_algebra_func_area_level_2_2_486
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(1x^2 + 1x + 5) - 1)/(-1(1x^2 + 1x + 5) + 3)) - 1 and g(x) = 4(3cos(1πx + 3) - 1) - 4 between the vertical lines x = 1.4 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14.0
|
math
|
train
| 160,551 |
math_algebra_func_area_level_2_2_487
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1((3(-2x^2 + 4x + 5) + 1)/(2(-2x^2 + 4x + 5) + 3)) + 1)/(3((3(-2x^2 + 4x + 5) + 1)/(2(-2x^2 + 4x + 5) + 3)) - 1), g(x) = 1sin(2π(-3|x + 3| + 3) - 2) - 3, x = -0.9, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.7
|
math
|
train
| 160,552 |
math_algebra_func_area_level_2_2_488
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(3(-1|x + 1| + 3)) - 1, g(x) = 4(-1|x| + 3)^2 - 3(-1|x| + 3) - 3, x = 1.9, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.7
|
math
|
train
| 160,553 |
math_algebra_func_area_level_2_2_489
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(1(3e^(1x) + 3) - 2) + 5 and g(x) = 4(3x^2 + 1x - 4)^2 + 4(3x^2 + 1x - 4) - 2 from x = -1.5 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.2
|
math
|
train
| 160,554 |
math_algebra_func_area_level_2_2_490
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(-2|x + 1| + 2) + 1) - 3)/(-3(1(-2|x + 1| + 2) + 1) - 2) and g(x) = (-2(-2x - 1) - 2)/(3(-2x - 1)) between the vertical lines x = -3.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.2
|
math
|
train
| 160,555 |
math_algebra_func_area_level_2_2_491
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(5(-5x + 3)) - 2| - 2 and g(x) = (3((3x + 1)/(-3x - 2)) + 2)/(-3((3x + 1)/(-3x - 2)) + 2) from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,556 |
math_algebra_func_area_level_2_2_492
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-1|(-1|x + 2| - 3) + 2| + 3)^2 - 3(-1|(-1|x + 2| - 3) + 2| + 3) - 2 and g(x) = 4((-2x - 2)/(3x + 1)) - 1 from x = -3.7 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
63.9
|
math
|
train
| 160,557 |
math_algebra_func_area_level_2_2_493
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(-2|(-3|x| + 2) + 2| + 2) - 1, g(x) = 2cos(3π(2x^2 + 1x - 1)) + 2, x = 1.9, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,558 |
math_algebra_func_area_level_2_2_494
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(4(1x^2 + 1x - 4) + 4) - 1 and g(x) = 3|(2cos(3πx - 2) + 1)| - 2 between the vertical lines x = -2.3 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82.5
|
math
|
train
| 160,559 |
math_algebra_func_area_level_2_2_495
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-3|(1cos(3πx + 1) - 1) + 1|)^2 - 3(-3|(1cos(3πx + 1) - 1) + 1|) - 5, g(x) = -4(3x^2 + 5x) + 4, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 160,560 |
math_algebra_func_area_level_2_2_496
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1((1x + 2)/(-2x))^2 + 5((1x + 2)/(-2x)) + 5) + 2| + 1 and g(x) = -3(-2x - 1)^2 + 2(-2x - 1) + 2 from x = -1.8 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.1
|
math
|
train
| 160,561 |
math_algebra_func_area_level_2_2_497
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(1sin(3π(-3|x| - 3) - 3) - 2)^2 - 3(1sin(3π(-3|x| - 3) - 3) - 2) - 5, g(x) = (-1(-3x + 4) - 3)/(-3(-3x + 4) - 1), x = 1.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
math
|
train
| 160,562 |
math_algebra_func_area_level_2_2_498
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(3sin(3π(-3x - 4) - 3) - 2)^2 - 4(3sin(3π(-3x - 4) - 3) - 2) - 3 and g(x) = -1(1cos(3πx - 3) + 2) + 1 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 160,563 |
math_algebra_func_area_level_2_2_499
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-1|(2|x + 2| + 3) - 1| - 1) + 5, g(x) = 4(1x^2 - 1x - 4) + 1, x = -1.6, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32.2
|
math
|
train
| 160,564 |
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