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_400
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π(-2|x| - 2) + 1) + 1 and g(x) = 3|x - 2| from x = 1.8 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 400 |
math_algebra_func_area_level_1_1_401
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((1x - 2)/(2x - 3)) - 1, g(x) = (1x + 1)/(-3x + 1), x = 0.5, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17.0
|
math
|
train
| 401 |
math_algebra_func_area_level_1_1_402
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(2π(-1x^2 - 5x)) + 1 and g(x) = 1x^2 - 3 from x = 1.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 402 |
math_algebra_func_area_level_1_1_403
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(1π((3x + 3)/(-1x + 2))) - 3, g(x) = -1x - 1, x = 1.6, and x = 1.7000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 403 |
math_algebra_func_area_level_1_1_404
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3sin(2πx + 3) - 1)^2 + 1(-3sin(2πx + 3) - 1) + 4 and g(x) = 2x between the vertical lines x = 3.9 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 404 |
math_algebra_func_area_level_1_1_405
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-4x^2 + 5x + 1) + 2 and g(x) = 2|x + 3| + 1 between the vertical lines x = 0.2 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 405 |
math_algebra_func_area_level_1_1_406
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-2cos(2πx - 1) - 3)^2 + 4(-2cos(2πx - 1) - 3) + 2, g(x) = 2x^2 - 4x - 1, x = 1.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 406 |
math_algebra_func_area_level_1_1_407
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2π(-1x + 1) + 3) + 2 and g(x) = 3|x| + 1 between the vertical lines x = -1.2 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
math
|
train
| 407 |
math_algebra_func_area_level_1_1_408
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-5x - 4) + 3)/(-1(-5x - 4) - 2) and g(x) = 1x + 2 between the vertical lines x = -3.1 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10.3
|
math
|
train
| 408 |
math_algebra_func_area_level_1_1_409
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3cos(1πx) - 2) and g(x) = 5x + 1 between the vertical lines x = -1.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.2
|
math
|
train
| 409 |
math_algebra_func_area_level_1_1_410
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(1π((2x)/(2x + 1)) - 2) + 2, g(x) = (-1x + 1)/(-1x - 1), x = -1.6, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32.5
|
math
|
train
| 410 |
math_algebra_func_area_level_1_1_411
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(-3cos(2πx - 1) + 1)^2 + 2(-3cos(2πx - 1) + 1) + 5 and g(x) = 2|x + 1| - 1 from x = 0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.0
|
math
|
train
| 411 |
math_algebra_func_area_level_1_1_412
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(1π(2|x| + 1) + 2) - 1, g(x) = (-2x - 2)/(3x), x = 2.4, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 412 |
math_algebra_func_area_level_1_1_413
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|x - 3| + 3) - 3)/(-2(-1|x - 3| + 3) - 3) and g(x) = -3x^2 + 3 from x = -0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.1
|
math
|
train
| 413 |
math_algebra_func_area_level_1_1_414
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(3e^(-1x) - 1) - 3)/(-3(3e^(-1x) - 1) - 3), g(x) = -5x^2 + 5x + 4, x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.4
|
math
|
train
| 414 |
math_algebra_func_area_level_1_1_415
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(2π(3x^2 - 2x + 1) + 2) - 3, g(x) = (-3x - 2)/(2x - 3), x = -4.0, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 415 |
math_algebra_func_area_level_1_1_416
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1sin(2πx + 1) + 1)^2 - 5(-1sin(2πx + 1) + 1) - 3 and g(x) = -3|x + 2| + 1 between the vertical lines x = -3.8 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
| 416 |
math_algebra_func_area_level_1_1_417
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|x - 2| + 3) + 1|, g(x) = 4x^2 + 4x - 1, x = -2.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7.7
|
math
|
train
| 417 |
math_algebra_func_area_level_1_1_418
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(1πx) - 2) - 1)/(1(-3cos(1πx) - 2)) and g(x) = (1x - 3)/(-1x - 3) between the vertical lines x = 3.0 and x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.0
|
math
|
train
| 418 |
math_algebra_func_area_level_1_1_419
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π(1x - 2) - 2) + 2, g(x) = 3x^2 - 5x - 5, x = -0.7, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21.8
|
math
|
train
| 419 |
math_algebra_func_area_level_1_1_420
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-3sin(2πx - 1) + 2) + 1, g(x) = -3x^2 - 3x + 4, x = -0.4, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.5
|
math
|
train
| 420 |
math_algebra_func_area_level_1_1_421
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1x - 2) - 1 and g(x) = (2x - 3)/(-1x + 2) between the vertical lines x = 1.6 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
45.7
|
math
|
train
| 421 |
math_algebra_func_area_level_1_1_422
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1|x + 1| - 3) + 2)/(2(1|x + 1| - 3) - 1) and g(x) = -2|x| - 2 between the vertical lines x = -4.5 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31.9
|
math
|
train
| 422 |
math_algebra_func_area_level_1_1_423
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-2|x + 2| + 2) + 2)/(-1(-2|x + 2| + 2)) and g(x) = -3x^2 - 2x from x = -0.7 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
math
|
train
| 423 |
math_algebra_func_area_level_1_1_424
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-4x - 3) - 2| + 1, g(x) = 2|x + 1| + 3, x = -2.5, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.2
|
math
|
train
| 424 |
math_algebra_func_area_level_1_1_425
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(1π(2x - 4) + 1) + 2, g(x) = -2x + 3, x = 1.0, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.0
|
math
|
train
| 425 |
math_algebra_func_area_level_1_1_426
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(3π(-1x) - 1) + 1 and g(x) = 5x + 2 from x = -0.6 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 426 |
math_algebra_func_area_level_1_1_427
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(3|x + 1| - 1)^2 - 4(3|x + 1| - 1) - 1 and g(x) = (-2x)/(3x - 2) from x = -2.7 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.2
|
math
|
train
| 427 |
math_algebra_func_area_level_1_1_428
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-2x + 4)^2 - 2 and g(x) = -2|x| + 2 from x = 1.5 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
| 428 |
math_algebra_func_area_level_1_1_429
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(2x^2 - 5x - 2) + 3)/(1(2x^2 - 5x - 2) - 3) and g(x) = 2x^2 - 1x - 5 from x = -1.2 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7.9
|
math
|
train
| 429 |
math_algebra_func_area_level_1_1_430
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-3cos(1πx + 1))^2 + 2(-3cos(1πx + 1)) and g(x) = (2x)/(-2x + 1) from x = -4.7 to x = -4.6000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 430 |
math_algebra_func_area_level_1_1_431
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π(2x + 3) - 3) - 1 and g(x) = (-1x + 1)/(-3x + 4) between the vertical lines x = -0.4 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
math
|
train
| 431 |
math_algebra_func_area_level_1_1_432
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-5x^2 - 4x + 4) - 1| + 2 and g(x) = -2x + 3 between the vertical lines x = -1.5 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 432 |
math_algebra_func_area_level_1_1_433
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|x + 3| - 1) + 2 and g(x) = -2x^2 + 3x - 1 between the vertical lines x = -0.9 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36.8
|
math
|
train
| 433 |
math_algebra_func_area_level_1_1_434
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-1cos(2πx + 2) - 3)| - 1 and g(x) = 1x + 1 from x = 0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 434 |
math_algebra_func_area_level_1_1_435
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(1π((2x - 3)/(2x - 1)) + 3) + 3, g(x) = -4x^2 - 3x + 1, x = -0.0, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 435 |
math_algebra_func_area_level_1_1_436
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-2|x - 2| - 2)^2 + 3(-2|x - 2| - 2) - 2, g(x) = 1|x + 3| + 2, x = 0.7, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19.7
|
math
|
train
| 436 |
math_algebra_func_area_level_1_1_437
|
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 + 4x + 3) - 1) - 2 and g(x) = -2x^2 - 2x + 4 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 437 |
math_algebra_func_area_level_1_1_438
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-3sin(1πx) - 2) + 1)/(1(-3sin(1πx) - 2)) and g(x) = -2|x - 3| - 1 from x = -0.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.1
|
math
|
train
| 438 |
math_algebra_func_area_level_1_1_439
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-2x)/(-3x + 4)) - 1| + 2 and g(x) = -1x^2 + 1x + 4 between the vertical lines x = -0.7 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.1
|
math
|
train
| 439 |
math_algebra_func_area_level_1_1_440
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π((1x + 1)/(3x)) + 2) - 3 and g(x) = -3|x| + 3 between the vertical lines x = -2.4 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10.1
|
math
|
train
| 440 |
math_algebra_func_area_level_1_1_441
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(1cos(1πx - 3)) + 4, g(x) = -1x^2 + 1, x = 0.8, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 441 |
math_algebra_func_area_level_1_1_442
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(3|x - 2| - 2) - 1, g(x) = 3x + 3, x = 0.7, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32.0
|
math
|
train
| 442 |
math_algebra_func_area_level_1_1_443
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((2x + 1)/(1x - 3)) - 2)/(3((2x + 1)/(1x - 3)) + 1), g(x) = -1|x - 2| + 1, x = -0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24.9
|
math
|
train
| 443 |
math_algebra_func_area_level_1_1_444
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((-3x - 2)/(2x)) - 3| and g(x) = -5x + 2 from x = -1.0 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 444 |
math_algebra_func_area_level_1_1_445
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-1x - 4) - 1)/(3(-1x - 4) + 1) and g(x) = 2x^2 - 5x + 1 from x = 0.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.1
|
math
|
train
| 445 |
math_algebra_func_area_level_1_1_446
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-5x^2 + 4) - 3| + 2 and g(x) = 3|x + 3| + 1 between the vertical lines x = -0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.4
|
math
|
train
| 446 |
math_algebra_func_area_level_1_1_447
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(1x^2 + 4x + 4) - 1| - 1, g(x) = 2|x - 2| - 2, x = -4.2, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17.6
|
math
|
train
| 447 |
math_algebra_func_area_level_1_1_448
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-3|x + 2| + 3) - 1)/(-1(-3|x + 2| + 3) + 2) and g(x) = -5x + 4 from x = -1.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.7
|
math
|
train
| 448 |
math_algebra_func_area_level_1_1_449
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4((3x + 2)/(3x + 3))^2 - 5((3x + 2)/(3x + 3)) - 4 and g(x) = 4x + 5 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"
}
] |
-6.5
|
math
|
train
| 449 |
math_algebra_func_area_level_1_1_450
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(2πx - 3)) - 1)/(-1(-3cos(2πx - 3))) and g(x) = (1x - 3)/(-1x + 2) from x = 3.2 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.9
|
math
|
train
| 450 |
math_algebra_func_area_level_1_1_451
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(-1|x - 3| + 3) + 3) and g(x) = -2x^2 + 5x - 3 between the vertical lines x = 0.5 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 451 |
math_algebra_func_area_level_1_1_452
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3π(5x - 5) + 1) + 3 and g(x) = 4x^2 - 5 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 452 |
math_algebra_func_area_level_1_1_453
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(-1sin(1πx + 2) + 3) - 3| - 1, g(x) = 4x^2 - 2x, x = -0.4, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 453 |
math_algebra_func_area_level_1_1_454
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(1|x + 3| - 2)^2 + 4 and g(x) = 5x^2 + 1x - 4 from x = -1.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9.1
|
math
|
train
| 454 |
math_algebra_func_area_level_1_1_455
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(3π(1x^2 - 2x + 1) - 3) + 2, g(x) = 1x^2 + 5x - 4, 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"
}
] |
0.1
|
math
|
train
| 455 |
math_algebra_func_area_level_1_1_456
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-3sin(1πx - 3)) - 3| + 1 and g(x) = (2x - 3)/(-2x + 3) from x = -3.9 to x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 456 |
math_algebra_func_area_level_1_1_457
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-4x^2 - 3x + 3)) and g(x) = -1x^2 + 1x + 3 between the vertical lines x = 0.6 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
math
|
train
| 457 |
math_algebra_func_area_level_1_1_458
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3sin(1πx - 1) - 2) + 1)/(2(3sin(1πx - 1) - 2) + 1) and g(x) = 3|x| - 1 between the vertical lines x = -3.5 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.9
|
math
|
train
| 458 |
math_algebra_func_area_level_1_1_459
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(1(3x^2 - 2x - 5)) + 1 and g(x) = -3x - 5 between the vertical lines x = -1.0 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19.4
|
math
|
train
| 459 |
math_algebra_func_area_level_1_1_460
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(5x^2 + 4x - 2) and g(x) = 3x + 5 from x = -1.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20.2
|
math
|
train
| 460 |
math_algebra_func_area_level_1_1_461
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(2cos(3πx - 1) + 1)^2 - 1(2cos(3πx - 1) + 1) - 4 and g(x) = -4x^2 - 1x + 1 from x = 0.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.4
|
math
|
train
| 461 |
math_algebra_func_area_level_1_1_462
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3((1x)/(2x - 1)) - 1)/(-1((1x)/(2x - 1)) + 2) and g(x) = 1x^2 - 5x + 3 from x = 1.6 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.6
|
math
|
train
| 462 |
math_algebra_func_area_level_1_1_463
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(1((2x - 3)/(3x))) + 3 and g(x) = (2x - 3)/(1x - 2) between the vertical lines x = 0.9 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 463 |
math_algebra_func_area_level_1_1_464
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(3sin(3πx - 2) - 1), g(x) = 1x^2 - 2x + 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"
}
] |
1.7
|
math
|
train
| 464 |
math_algebra_func_area_level_1_1_465
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(1π(1|x| + 3) - 1) - 1 and g(x) = -2x^2 + 5x - 2 from x = -0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 465 |
math_algebra_func_area_level_1_1_466
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(2x - 2)^2 - 1(2x - 2) + 5 and g(x) = 1|x| - 3 from x = 0.2 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.4
|
math
|
train
| 466 |
math_algebra_func_area_level_1_1_467
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(2π((-2x + 3)/(-1x - 3)) + 1) + 3, g(x) = 3x + 4, 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"
}
] |
0.1
|
math
|
train
| 467 |
math_algebra_func_area_level_1_1_468
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|x| + 2) - 3)/(-2(-1|x| + 2)), g(x) = -5x - 3, x = -1.6, 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
| 468 |
math_algebra_func_area_level_1_1_469
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2cos(3π(-3|x|) + 3) + 1 and g(x) = -2|x - 2| + 3 from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 469 |
math_algebra_func_area_level_1_1_470
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(3π(1x^2 - 1x + 5) - 1) + 1, g(x) = 4x + 5, x = -1.1, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 470 |
math_algebra_func_area_level_1_1_471
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π(3x + 2) - 3) + 1 and g(x) = 1|x + 2| - 3 between the vertical lines x = 1.7 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 471 |
math_algebra_func_area_level_1_1_472
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(-2x - 1) + 1) + 2 and g(x) = 1x^2 - 1x + 3 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
| 472 |
math_algebra_func_area_level_1_1_473
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(2π(-4x^2 - 2x - 1) + 1) - 3 and g(x) = (3x + 1)/(1x + 2) from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 473 |
math_algebra_func_area_level_1_1_474
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(3sin(1πx - 1) - 3) - 2)/(1(3sin(1πx - 1) - 3) + 3), g(x) = (2x - 1)/(-1x + 2), x = 0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 474 |
math_algebra_func_area_level_1_1_475
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-2cos(3πx - 3) - 2) - 1| - 2 and g(x) = 4x^2 - 1x from x = -0.5 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 475 |
math_algebra_func_area_level_1_1_476
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(4x - 1)^2 + 5(4x - 1) - 1 and g(x) = -2|x - 2| + 2 from x = 0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 476 |
math_algebra_func_area_level_1_1_477
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1e^(1(3|x - 2|)), g(x) = 2x^2 + 5x + 3, x = 1.2, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33.5
|
math
|
train
| 477 |
math_algebra_func_area_level_1_1_478
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(1|x - 2| - 2) - 3 and g(x) = 1x - 4 from x = -0.5 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9.4
|
math
|
train
| 478 |
math_algebra_func_area_level_1_1_479
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3π((3x + 1)/(-1x + 3)) + 1) + 2 and g(x) = (-1x + 3)/(2x + 3) between the vertical lines x = 1.9 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 479 |
math_algebra_func_area_level_1_1_480
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2((1x - 1)/(-3x - 1)) + 4, g(x) = 4x^2 + 2x - 4, x = -1.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
math
|
train
| 480 |
math_algebra_func_area_level_1_1_481
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2e^(-2(-3x^2 + 4)) + 3 and g(x) = -5x^2 - 2x + 5 from x = -0.9 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.0
|
math
|
train
| 481 |
math_algebra_func_area_level_1_1_482
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(2π(2x + 4) + 1), g(x) = -1x^2 + 5x, x = -0.1, 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
| 482 |
math_algebra_func_area_level_1_1_483
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(1x^2 + 5x - 4) - 1)/(-1(1x^2 + 5x - 4) - 2) and g(x) = 3x - 3 from x = 0.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 483 |
math_algebra_func_area_level_1_1_484
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(1x + 2) - 1, g(x) = (1x - 1)/(2x - 1), x = -2.8, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17.0
|
math
|
train
| 484 |
math_algebra_func_area_level_1_1_485
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2πx + 1)) - 5 and g(x) = 3x^2 - 3x - 1 between the vertical lines x = 0.6 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.2
|
math
|
train
| 485 |
math_algebra_func_area_level_1_1_486
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(2π((2x + 2)/(-2x)) + 3) and g(x) = 3|x + 3| from x = -3.2 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
| 486 |
math_algebra_func_area_level_1_1_487
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1cos(3πx + 2) + 3) - 1| - 3 and g(x) = 2x + 5 between the vertical lines x = -1.3 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 487 |
math_algebra_func_area_level_1_1_488
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-5x^2 + 2x + 5) + 1 and g(x) = -5x^2 - 1x + 1 between the vertical lines x = -0.9 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40.7
|
math
|
train
| 488 |
math_algebra_func_area_level_1_1_489
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(1πx + 1) + 2) + 1, g(x) = 5x^2 - 1x - 5, x = -1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13.8
|
math
|
train
| 489 |
math_algebra_func_area_level_1_1_490
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1π(3x^2 - 4x - 3) + 2) and g(x) = -1|x + 1| between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 490 |
math_algebra_func_area_level_1_1_491
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2((-3x - 1)/(-1x - 3)) + 1)/(2((-3x - 1)/(-1x - 3)) + 2) and g(x) = -2|x + 1| + 2 from x = -0.6 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 491 |
math_algebra_func_area_level_1_1_492
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-1((-1x + 1)/(-1x + 3))) - 1 and g(x) = 4x + 1 between the vertical lines x = -0.3 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.1
|
math
|
train
| 492 |
math_algebra_func_area_level_1_1_493
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-2sin(1πx - 3) + 1)^2 - 3(-2sin(1πx - 3) + 1) - 3, g(x) = 3x + 1, x = -3.1, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.1
|
math
|
train
| 493 |
math_algebra_func_area_level_1_1_494
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4((-1x + 3)/(-1x + 2))^2 + 5((-1x + 3)/(-1x + 2)) + 5, g(x) = 3x^2 + 3x + 3, x = -1.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.0
|
math
|
train
| 494 |
math_algebra_func_area_level_1_1_495
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(5x - 3) - 3)/(2(5x - 3)) and g(x) = -2x + 5 between the vertical lines x = 0.5 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.5
|
math
|
train
| 495 |
math_algebra_func_area_level_1_1_496
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(1|x - 1| + 2) + 1) - 2 and g(x) = (1x + 2)/(-2x - 1) between the vertical lines x = -4.7 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
| 496 |
math_algebra_func_area_level_1_1_497
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-3x^2 + 2x) - 3, g(x) = -2x^2 - 3, x = 0.0, 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
| 497 |
math_algebra_func_area_level_1_1_498
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(3πx + 1)) - 3 and g(x) = 3x + 5 between the vertical lines x = -3.0 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 498 |
math_algebra_func_area_level_1_1_499
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(2cos(3πx - 3) + 2) - 1| + 2 and g(x) = 2x + 2 from x = 0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.2
|
math
|
train
| 499 |
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