id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_3_3_600
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(2(-3|(2x + 1)| - 2))^2 - 2(2(-3|(2x + 1)| - 2)) and g(x) = 1(-2|(-1x^2 + 2x - 4)|)^2 - 4(-2|(-1x^2 + 2x - 4)|) between the vertical lines x = -1.1 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
57.7
|
math
|
train
|
math_algebra_func_area_level_3_3_601
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1((-1(3|(-1x^2 - 3x - 4) - 2| - 3) - 2)/(-3(3|(-1x^2 - 3x - 4) - 2| - 3) + 4))^2 + 5((-1(3|(-1x^2 - 3x - 4) - 2| - 3) - 2)/(-3(3|(-1x^2 - 3x - 4) - 2| - 3) + 4)) + 5, g(x) = (1(-1(-5x^2 - 5x - 1) - 2) - 2)/(1(-1(-5x^2 - 5x - 1) - 2)), x = -1.1, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.0
|
math
|
train
|
math_algebra_func_area_level_3_3_602
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-1(-2|(-2x^2 + 2x + 1) + 1| - 3)^2 - 3(-2|(-2x^2 + 2x + 1) + 1| - 3) + 1) - 2)/(-3(-1(-2|(-2x^2 + 2x + 1) + 1| - 3)^2 - 3(-2|(-2x^2 + 2x + 1) + 1| - 3) + 1) - 2) and g(x) = (-2((-2(-2|x - 3|) - 2)/(1(-2|x - 3|) + 1)) - 3)/(-3((-2(-2|x - 3|) - 2)/(1(-2|x - 3|) + 1)) + 1) from x = -0.7 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_603
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(3π(-1((1(-2x^2 + 3x + 1) - 2)/(2(-2x^2 + 3x + 1) + 2))^2 + 3((1(-2x^2 + 3x + 1) - 2)/(2(-2x^2 + 3x + 1) + 2))) - 2) - 1 and g(x) = (-2(3|((3x - 2)/(2x + 1)) - 3| - 2) + 3)/(3(3|((3x - 2)/(2x + 1)) - 3| - 2) - 2) from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_604
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(3(-1|(1x + 3) - 1| + 3) + 1) - 2| + 2, g(x) = (3(1|(-1x - 1) + 1| - 3) - 2)/(2(1|(-1x - 1) + 1| - 3) + 3), x = -1.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.4
|
math
|
train
|
math_algebra_func_area_level_3_3_605
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(1((-2(-4x^2 + 5x - 3) + 3)/(-3(-4x^2 + 5x - 3) - 3)) - 2) + 3, g(x) = 4(-3(-5x + 5) - 2)^2 - 4(-3(-5x + 5) - 2), x = 1.1, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_606
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3((2(-3e^(1(-3x^2 - 2x - 3)) + 2) - 3)/(-3(-3e^(1(-3x^2 - 2x - 3)) + 2) - 1)) + 1)/(3((2(-3e^(1(-3x^2 - 2x - 3)) + 2) - 3)/(-3(-3e^(1(-3x^2 - 2x - 3)) + 2) - 1)) + 2), g(x) = (-2(2sin(3π(1|x + 2| - 2) + 3) - 1) + 2)/(2(2sin(3π(1|x + 2| - 2) + 3) - 1) - 1), x = -0.8, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_3_3_607
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-1(-2|((-2x - 1)/(-3x - 1)) - 1|) - 3) + 2 and g(x) = 2sin(2π(-4((-3x + 1)/(1x)) + 2) - 2) + 2 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_608
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(3cos(2π(-1((3x - 3)/(-3x + 2))^2 + 2((3x - 3)/(-3x + 2))) - 3) + 1)^2 + 3(3cos(2π(-1((3x - 3)/(-3x + 2))^2 + 2((3x - 3)/(-3x + 2))) - 3) + 1) and g(x) = 1(2(2e^(-2x) - 2)^2 + 3(2e^(-2x) - 2) - 1) + 2 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_609
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(3sin(1π(-3((-1x - 3)/(-3x + 4)) - 4) - 1) - 3)^2 - 2(3sin(1π(-3((-1x - 3)/(-3x + 4)) - 4) - 1) - 3) + 1 and g(x) = -4(-1sin(1π(-1x - 3)) - 1) - 4 from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_610
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-2((-3(2|x - 3| + 3) - 2)/(-2(2|x - 3| + 3) + 3)) + 3) - 1)/(2(-2((-3(2|x - 3| + 3) - 2)/(-2(2|x - 3| + 3) + 3)) + 3) - 1) and g(x) = -5(3cos(1π((2x + 2)/(-2x - 1)) + 2) - 2) + 4 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}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_3_3_611
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-3(2|(3e^(-1x) - 1) - 1|) + 2) + 1)/(1(-3(2|(3e^(-1x) - 1) - 1|) + 2) - 2) and g(x) = (2(5(2e^(1x) + 2)^2 - 5(2e^(1x) + 2) - 3) - 1)/(-3(5(2e^(1x) + 2)^2 - 5(2e^(1x) + 2) - 3) + 4) between the vertical lines x = 0.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.1
|
math
|
train
|
math_algebra_func_area_level_3_3_612
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-3(2|(2sin(3πx - 2) - 1)| - 1)^2 + 4(2|(2sin(3πx - 2) - 1)| - 1) + 4) + 2 and g(x) = 3|(1cos(3π((-1x - 2)/(2x + 1))) - 1) - 2| + 1 from x = -3.1 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_613
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1sin(3π(-2|(-1(-4x - 1) + 3) - 3| - 1) - 2) - 3 and g(x) = -4(-4((-1x - 1)/(2x - 1))^2 - 5((-1x - 1)/(2x - 1)) + 3) - 3 from x = -0.3 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-49.1
|
math
|
train
|
math_algebra_func_area_level_3_3_614
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-2|(1((1x + 2)/(2x + 3))^2 - 3((1x + 2)/(2x + 3)) - 1) - 2| - 3)^2 - 4(-2|(1((1x + 2)/(2x + 3))^2 - 3((1x + 2)/(2x + 3)) - 1) - 2| - 3) - 1 and g(x) = 3|(-5(2|x + 3| + 2) + 1) - 3| + 1 from x = -1.4 to x = -1.2999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
71.0
|
math
|
train
|
math_algebra_func_area_level_3_3_615
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2cos(3π(-5(-5(-3|x| - 3) - 1)^2 - 3(-5(-3|x| - 3) - 1) + 2) + 3) + 1 and g(x) = 3(-3(5x^2 - 3x - 4) - 5) + 1 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_616
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(1((1(-3cos(3πx - 1) + 3) + 2)/(-2(-3cos(3πx - 1) + 3) - 1))^2 - 2) - 2)/(3(1((1(-3cos(3πx - 1) + 3) + 2)/(-2(-3cos(3πx - 1) + 3) - 1))^2 - 2) - 1) and g(x) = -1|((2(-3cos(2πx + 2)) - 1)/(3(-3cos(2πx + 2)) + 3))| - 2 from x = 0.1 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.4
|
math
|
train
|
math_algebra_func_area_level_3_3_617
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1cos(1π(3|(1(-2|x| + 1)^2 - 2) - 2| + 1) + 2) - 2, g(x) = -2|((-1(-1x + 4))/(-3(-1x + 4) - 1)) - 2|, x = 4.5, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_618
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(-2(-2|x + 3|) - 2)^2 + 1(-2(-2|x + 3|) - 2) - 4) + 1)/(1(-1(-2(-2|x + 3|) - 2)^2 + 1(-2(-2|x + 3|) - 2) - 4)) and g(x) = -1|(-3(-3x + 3)^2 + 5(-3x + 3) + 1) - 1| + 3 between the vertical lines x = 0.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.4
|
math
|
train
|
math_algebra_func_area_level_3_3_619
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1((-1(2(1sin(3πx - 2))^2 - 4(1sin(3πx - 2)) - 3) + 1)/(-2(2(1sin(3πx - 2))^2 - 4(1sin(3πx - 2)) - 3) + 1)) + 1)/(3((-1(2(1sin(3πx - 2))^2 - 4(1sin(3πx - 2)) - 3) + 1)/(-2(2(1sin(3πx - 2))^2 - 4(1sin(3πx - 2)) - 3) + 1)) + 1) and g(x) = -1(-4(3e^(2x) - 1)^2 + 1(3e^(2x) - 1) + 5)^2 + 4(-4(3e^(2x) - 1)^2 + 1(3e^(2x) - 1) + 5) - 1 from x = -1.9 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_620
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(2|(4(1x^2 + 2x - 5)^2 + 5(1x^2 + 2x - 5) - 2) + 2| + 3) + 1| - 3, g(x) = 2(2e^(-2((-3x + 3)/(2x - 1))))^2 - 5(2e^(-2((-3x + 3)/(2x - 1)))) + 5, x = 1.1, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
130.6
|
math
|
train
|
math_algebra_func_area_level_3_3_621
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-2|((-2(-3e^(-1x)) - 1)/(-1(-3e^(-1x)) + 2)) - 2| - 1)^2 + 5(-2|((-2(-3e^(-1x)) - 1)/(-1(-3e^(-1x)) + 2)) - 2| - 1) + 1 and g(x) = (2((2(-3cos(3πx - 2)) - 2)/(1(-3cos(3πx - 2)))) - 3)/(-1((2(-3cos(3πx - 2)) - 2)/(1(-3cos(3πx - 2)))) + 2) from x = -3.1 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.4
|
math
|
train
|
math_algebra_func_area_level_3_3_622
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(4(4(3x + 2)^2 + 3(3x + 2) + 5)^2 + 1(4(3x + 2)^2 + 3(3x + 2) + 5) - 2) + 1)/(-1(4(4(3x + 2)^2 + 3(3x + 2) + 5)^2 + 1(4(3x + 2)^2 + 3(3x + 2) + 5) - 2) - 3) and g(x) = 4(-2(2|x + 3| - 1) + 1)^2 - 3(-2(2|x + 3| - 1) + 1) - 3 between the vertical lines x = -3.3 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.2
|
math
|
train
|
math_algebra_func_area_level_3_3_623
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-3|(-1|(-2e^(1x) - 3) + 2| - 2)| - 2))/(-1(-3|(-1|(-2e^(1x) - 3) + 2| - 2)| - 2) + 2), g(x) = (1(-1|((-1x)/(1x + 2)) + 2| + 3) + 1)/(-1(-1|((-1x)/(1x + 2)) + 2| + 3) + 3), x = -2.6, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_3_3_624
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(1(2cos(2π(-2x + 5)) - 2)^2 + 5(2cos(2π(-2x + 5)) - 2) + 4))/(-2(1(2cos(2π(-2x + 5)) - 2)^2 + 5(2cos(2π(-2x + 5)) - 2) + 4) + 1) and g(x) = 2e^(1((-1((1x + 1)/(1x)) - 3)/(-2((1x + 1)/(1x)) - 2))) + 1 between the vertical lines x = -4.1 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_3_3_625
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2((1(-1(3|x + 2| + 1)^2 + 3(3|x + 2| + 1) - 1) + 3)/(-1(-1(3|x + 2| + 1)^2 + 3(3|x + 2| + 1) - 1) - 2)) + 3)/(2((1(-1(3|x + 2| + 1)^2 + 3(3|x + 2| + 1) - 1) + 3)/(-1(-1(3|x + 2| + 1)^2 + 3(3|x + 2| + 1) - 1) - 2)) + 3) and g(x) = -2(1(2x^2 + 2x + 1) - 4) + 3 from x = -2.0 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.0
|
math
|
train
|
math_algebra_func_area_level_3_3_626
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3((-1(-2cos(1π((1x + 1)/(-1x - 3)) + 1) + 1) + 1)/(2(-2cos(1π((1x + 1)/(-1x - 3)) + 1) + 1) - 3)) - 2 and g(x) = -1sin(3π(3((-1x - 1)/(-2x + 3)) + 5) + 3) + 2 from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_627
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(-3sin(2π(3|(3x^2 + 2x)| - 1) + 1) + 1) - 2)/(-2(-3sin(2π(3|(3x^2 + 2x)| - 1) + 1) + 1) + 3) and g(x) = 5(2sin(1π(1x + 2) + 1) + 3)^2 - 3(2sin(1π(1x + 2) + 1) + 3) - 1 from x = 3.3 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_628
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((-1(4(-3cos(1πx) - 1)^2 + 1(-3cos(1πx) - 1) + 2) + 2)/(-1(4(-3cos(1πx) - 1)^2 + 1(-3cos(1πx) - 1) + 2) - 3)) and g(x) = 3|(2cos(3π(1x^2 - 1x - 1) + 1) - 2) + 1| - 2 between the vertical lines x = 3.6 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_629
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((2(1(5x^2 + 3x + 5) - 3) + 2)/(1(1(5x^2 + 3x + 5) - 3) + 2)) + 4 and g(x) = -5(-2((2x + 2)/(3x - 2))^2 + 5((2x + 2)/(3x - 2)) + 2) - 2 between the vertical lines x = -0.2 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-72.6
|
math
|
train
|
math_algebra_func_area_level_3_3_630
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(1(-4(5x^2 + 4x - 1) + 3)^2) - 4, g(x) = (-1(3cos(1π(-4x - 1) - 3) - 2))/(-2(3cos(1π(-4x - 1) - 3) - 2) - 3), x = -1.1, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.9
|
math
|
train
|
math_algebra_func_area_level_3_3_631
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5((2((1(3x - 1))/(-3(3x - 1) - 3)) + 2)/(-3((1(3x - 1))/(-3(3x - 1) - 3)) + 2))^2 - 5((2((1(3x - 1))/(-3(3x - 1) - 3)) + 2)/(-3((1(3x - 1))/(-3(3x - 1) - 3)) + 2)) - 3 and g(x) = 5((2(1x^2 + 4x - 5) - 3)/(1(1x^2 + 4x - 5) + 1)) between the vertical lines x = 0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-4.4
|
math
|
train
|
math_algebra_func_area_level_3_3_632
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((3(-2|((-1x + 1)/(-1x - 2)) - 2| - 2) - 3)/(-2(-2|((-1x + 1)/(-1x - 2)) - 2| - 2) - 1))^2 + 4((3(-2|((-1x + 1)/(-1x - 2)) - 2| - 2) - 3)/(-2(-2|((-1x + 1)/(-1x - 2)) - 2| - 2) - 1)), g(x) = 4(2|(-3x^2 + 4x + 3) + 2| - 1)^2 - 3(2|(-3x^2 + 4x + 3) + 2| - 1) - 3, x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_633
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(-3cos(1π(3|(-3x^2 - 4x + 2)| + 1) + 3) - 2) + 2| - 1, g(x) = -3cos(1π(-1|(-2x - 3) - 2| + 1) + 1) - 1, x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_634
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|((2(-3cos(3π(-1x) - 2) - 2) - 2)/(-3(-3cos(3π(-1x) - 2) - 2) - 3)) + 3|, g(x) = (1(-3|((-1x + 1)/(-3x + 2))| - 3) + 3)/(2(-3|((-1x + 1)/(-3x + 2))| - 3) - 3), x = -4.4, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_635
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π(5((1((1x - 3)/(-2x)) + 1)/(-2((1x - 3)/(-2x)) + 1)) - 3) + 3) + 1 and g(x) = (-3(-2(-2x + 4)))/(-3(-2(-2x + 4)) - 2) between the vertical lines x = 1.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_636
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((3(-5(3|x - 1| - 2)^2 - 2(3|x - 1| - 2) + 4) - 1)/(-2(-5(3|x - 1| - 2)^2 - 2(3|x - 1| - 2) + 4) + 1))^2 + 1((3(-5(3|x - 1| - 2)^2 - 2(3|x - 1| - 2) + 4) - 1)/(-2(-5(3|x - 1| - 2)^2 - 2(3|x - 1| - 2) + 4) + 1)) - 5 and g(x) = -5(2(1|x - 3| + 1)^2 - 2(1|x - 3| + 1) - 1)^2 - 4(2(1|x - 3| + 1)^2 - 2(1|x - 3| + 1) - 1) - 4 between the vertical lines x = 1.9 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.7
|
math
|
train
|
math_algebra_func_area_level_3_3_637
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4((-3(5((-1x + 2)/(-1x + 2))^2 + 2((-1x + 2)/(-1x + 2)) + 2) - 1)/(3(5((-1x + 2)/(-1x + 2))^2 + 2((-1x + 2)/(-1x + 2)) + 2) + 1))^2 - 5((-3(5((-1x + 2)/(-1x + 2))^2 + 2((-1x + 2)/(-1x + 2)) + 2) - 1)/(3(5((-1x + 2)/(-1x + 2))^2 + 2((-1x + 2)/(-1x + 2)) + 2) + 1)) + 4, g(x) = 2|(1(1|x + 1| - 1)^2 + 4) + 2| + 1, x = -2.0, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_3_3_638
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-3(4((1x - 2)/(3x + 3)) - 4)^2 + 2(4((1x - 2)/(3x + 3)) - 4) + 3) + 2)/(3(-3(4((1x - 2)/(3x + 3)) - 4)^2 + 2(4((1x - 2)/(3x + 3)) - 4) + 3) + 1), g(x) = -3|((1(-1|x - 1| + 2) - 3)/(1(-1|x - 1| + 2))) - 2| + 1, x = -5.0, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.4
|
math
|
train
|
math_algebra_func_area_level_3_3_639
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2|(3|(-1|x + 3| + 2) + 1| - 2) + 2| - 3) - 1)/(-1(2|(3|(-1|x + 3| + 2) + 1| - 2) + 2| - 3) + 2) and g(x) = (-1((3(2x^2 - 4x + 1) + 1)/(3(2x^2 - 4x + 1) - 1)) + 1)/(2((3(2x^2 - 4x + 1) + 1)/(3(2x^2 - 4x + 1) - 1)) + 3) from x = -0.7 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_640
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(-3cos(1π(-2|((-1x - 3)/(-2x - 1)) + 3| - 1) - 3)) + 1 and g(x) = (-2(2((-2x)/(3x - 2)) - 4))/(1(2((-2x)/(3x - 2)) - 4) + 2) between the vertical lines x = -0.3 and x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_3_3_641
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-3(-5(-2|x - 2| - 1)^2 + 1(-2|x - 2| - 1) - 1)^2 + 2(-5(-2|x - 2| - 1)^2 + 1(-2|x - 2| - 1) - 1) - 3) + 2)/(1(-3(-5(-2|x - 2| - 1)^2 + 1(-2|x - 2| - 1) - 1)^2 + 2(-5(-2|x - 2| - 1)^2 + 1(-2|x - 2| - 1) - 1) - 3) - 3) and g(x) = -3|(-2|((2x)/(-1x + 3)) - 3|) + 2| + 2 from x = 1.6 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_3_3_642
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(2(1sin(2π(4x^2 - 4x)) - 1)^2 - 3(1sin(2π(4x^2 - 4x)) - 1)) - 3| - 1 and g(x) = -3|(-2|((2x - 3)/(2x - 1))| + 2) + 1| + 2 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_643
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(1(-1((2x + 3)/(1x - 2))^2 - 3((2x + 3)/(1x - 2)) + 3) - 4) + 3 and g(x) = -2|(-3cos(2π(-2x + 3)) - 2) + 3| - 2 from x = -3.1 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_644
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3((2(3|x + 2| - 1) + 1)/(1(3|x + 2| - 1) + 3)) + 4) - 1)/(1(3((2(3|x + 2| - 1) + 1)/(1(3|x + 2| - 1) + 3)) + 4)) and g(x) = 2cos(2π(2|(-2|x + 3|) + 2| - 1) - 3) - 1 from x = -3.6 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_645
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-1((-2(1sin(2πx) - 3) + 2)/(-3(1sin(2πx) - 3) - 2))^2 + 1((-2(1sin(2πx) - 3) + 2)/(-3(1sin(2πx) - 3) - 2)) + 2) - 1, g(x) = 3e^(-1((2(2|x - 2| + 2) - 1)/(1(2|x - 2| + 2) + 1))), x = -2.6, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_646
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((1(-2(3cos(3πx + 2) - 3)^2 - 5(3cos(3πx + 2) - 3) - 1) + 1)/(-1(-2(3cos(3πx + 2) - 3)^2 - 5(3cos(3πx + 2) - 3) - 1) + 3))^2 - 1((1(-2(3cos(3πx + 2) - 3)^2 - 5(3cos(3πx + 2) - 3) - 1) + 1)/(-1(-2(3cos(3πx + 2) - 3)^2 - 5(3cos(3πx + 2) - 3) - 1) + 3)) - 2, g(x) = 1(-5(1x^2 - 1x) + 3) - 3, x = 1.6, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_3_3_647
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-2|((3(2|x - 3| + 1) - 1)/(2(2|x - 3| + 1) - 1)) - 3| + 2) - 2)/(-2(-2|((3(2|x - 3| + 1) - 1)/(2(2|x - 3| + 1) - 1)) - 3| + 2) - 1) and g(x) = 2e^(-1((-2(-3x - 1) - 1)/(3(-3x - 1)))) from x = 2.9 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_648
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-1(5(-3sin(2πx + 2) + 2)^2 + 2(-3sin(2πx + 2) + 2) + 4)^2 + 1(5(-3sin(2πx + 2) + 2)^2 + 2(-3sin(2πx + 2) + 2) + 4) + 2))/(1(-1(5(-3sin(2πx + 2) + 2)^2 + 2(-3sin(2πx + 2) + 2) + 4)^2 + 1(5(-3sin(2πx + 2) + 2)^2 + 2(-3sin(2πx + 2) + 2) + 4) + 2) + 2) and g(x) = 1|((-3(-2e^(1x) + 2) + 3)/(-2(-2e^(1x) + 2) + 3)) + 1| + 1 between the vertical lines x = -1.0 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_649
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|((2(2(-4x^2 + 3x)^2 - 3(-4x^2 + 3x) - 2) - 1)/(2(2(-4x^2 + 3x)^2 - 3(-4x^2 + 3x) - 2) - 3)) - 1| - 1 and g(x) = 5(1(2x + 4)^2 - 3(2x + 4) + 1) - 2 from x = -1.8 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.8
|
math
|
train
|
math_algebra_func_area_level_3_3_650
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(5(3((1x - 3)/(2x)) + 5)^2 - 3(3((1x - 3)/(2x)) + 5) - 3) - 5 and g(x) = -2sin(2π(3(-1x - 3)^2 + 1(-1x - 3) + 5) - 2) - 1 from x = 0.6 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_3_3_651
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3cos(2π(3|(2|(-4x + 5) - 2| - 2) - 1| - 3) - 3) + 2 and g(x) = 2(3|(2cos(3πx + 3)) - 2| - 1) - 3 from x = -3.8 to x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_3_3_652
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(-3sin(1π((3(2|x - 1| + 2) - 2)/(3(2|x - 1| + 2) + 2)) - 2) - 1) + 2|, g(x) = (-1(2|(-1|x + 1| + 1)| - 2) + 2)/(-3(2|(-1|x + 1| + 1)| - 2)), x = 2.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_3_3_653
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(2e^(-2((2((2x + 1)/(-1x + 3)) - 1)/(2((2x + 1)/(-1x + 3))))) - 2)^2 + 1(2e^(-2((2((2x + 1)/(-1x + 3)) - 1)/(2((2x + 1)/(-1x + 3))))) - 2) - 4 and g(x) = (-1(-2(2|x| + 2)^2 - 4(2|x| + 2) + 4) + 3)/(1(-2(2|x| + 2)^2 - 4(2|x| + 2) + 4)) from x = 0.1 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_654
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(4((2(-1|x + 1| + 1) - 2)/(2(-1|x + 1| + 1) - 3))^2 + 3((2(-1|x + 1| + 1) - 2)/(2(-1|x + 1| + 1) - 3))) + 3| + 1 and g(x) = (2(-1(2cos(1πx))^2 + 4(2cos(1πx)) + 2) + 1)/(1(-1(2cos(1πx))^2 + 4(2cos(1πx)) + 2)) from x = 3.4 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.1
|
math
|
train
|
math_algebra_func_area_level_3_3_655
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(3(5((-2x - 2)/(-3x + 4)) + 4)^2 - 1(5((-2x - 2)/(-3x + 4)) + 4) - 1)^2 + 4(3(5((-2x - 2)/(-3x + 4)) + 4)^2 - 1(5((-2x - 2)/(-3x + 4)) + 4) - 1) + 1, g(x) = 1cos(1π(-1|(-3x^2 + 2)|)) + 2, x = 0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_656
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-5((-1(2x^2 - 2x + 1) + 1)/(-1(2x^2 - 2x + 1) - 1)))^2 - 4(-5((-1(2x^2 - 2x + 1) + 1)/(-1(2x^2 - 2x + 1) - 1))) + 4 and g(x) = 2(3cos(3π(-1x^2 + 1x - 3) + 2) + 3)^2 - 4(3cos(3π(-1x^2 + 1x - 3) + 2) + 3) - 3 between the vertical lines x = -0.3 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.7
|
math
|
train
|
math_algebra_func_area_level_3_3_657
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3sin(3π(4((3(-2|x + 2| - 1) - 2)/(2(-2|x + 2| - 1) - 1))^2 + 2((3(-2|x + 2| - 1) - 2)/(2(-2|x + 2| - 1) - 1))) + 2) + 1 and g(x) = (-2(2e^(-2(3x - 3)) + 1) + 1)/(2(2e^(-2(3x - 3)) + 1) + 3) from x = -1.0 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_658
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(1|(2(-3e^(-2x))^2 - 2) - 1| + 3)^2 - 3(1|(2(-3e^(-2x))^2 - 2) - 1| + 3) - 1 and g(x) = 5(3((2x + 1)/(3x + 3)) + 2)^2 - 5(3((2x + 1)/(3x + 3)) + 2) + 3 between the vertical lines x = 1.0 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_3_3_659
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-2(1(-3x^2 + 3x - 4) + 3) + 3) - 5 and g(x) = -4(3(-2cos(2πx + 1) + 3) - 3)^2 - 1(3(-2cos(2πx + 1) + 3) - 3) + 4 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_660
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1((-2((1(-5x^2 + 5x + 3) - 2)/(-2(-5x^2 + 5x + 3) + 3)))/(3((1(-5x^2 + 5x + 3) - 2)/(-2(-5x^2 + 5x + 3) + 3)) + 1)) + 2)/(-3((-2((1(-5x^2 + 5x + 3) - 2)/(-2(-5x^2 + 5x + 3) + 3)))/(3((1(-5x^2 + 5x + 3) - 2)/(-2(-5x^2 + 5x + 3) + 3)) + 1)) + 2) and g(x) = (-1(-1|(4x - 2)| + 2) + 2)/(2(-1|(4x - 2)| + 2) + 3) between the vertical lines x = -0.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_3_3_661
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(-1cos(2π(-1(-1|x - 3| - 3) + 1) - 1) + 2) + 3 and g(x) = 4(5(2e^(1x) - 3) + 5)^2 - 4(5(2e^(1x) - 3) + 5) - 2 between the vertical lines x = -0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.5
|
math
|
train
|
math_algebra_func_area_level_3_3_662
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(-1(1x^2 - 4x - 2) - 1) - 1)/(-1(-1(1x^2 - 4x - 2) - 1) - 1)) + 1)/(-2((-2(-1(1x^2 - 4x - 2) - 1) - 1)/(-1(-1(1x^2 - 4x - 2) - 1) - 1)) - 2) and g(x) = 1(1|(3|x + 3| - 2) + 1| - 3)^2 - 4(1|(3|x + 3| - 2) + 1| - 3) - 5 between the vertical lines x = -0.4 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_3_3_663
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3((-1(-2e^(-1(-2|x - 2| + 3))))/(-2(-2e^(-1(-2|x - 2| + 3))) - 2))^2 + 1((-1(-2e^(-1(-2|x - 2| + 3))))/(-2(-2e^(-1(-2|x - 2| + 3))) - 2)) - 3 and g(x) = 3(1(2x - 1)^2 + 4(2x - 1))^2 + 3(1(2x - 1)^2 + 4(2x - 1)) - 4 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_3_3_664
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((2(-1(2|x - 2|) + 4) - 2)/(1(-1(2|x - 2|) + 4)))^2 + 4((2(-1(2|x - 2|) + 4) - 2)/(1(-1(2|x - 2|) + 4))) + 4 and g(x) = -2sin(3π(5(2x) + 2) + 3) between the vertical lines x = 3.6 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_665
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-3((2(-2x + 1))/(-1(-2x + 1) + 3)) - 5)^2 - 4(-3((2(-2x + 1))/(-1(-2x + 1) + 3)) - 5) + 1, g(x) = -2(1e^(-2(-4x^2 + 2x + 2)) - 1) - 1, x = -1.1, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-3299.0
|
math
|
train
|
math_algebra_func_area_level_3_3_666
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(5(-1((-2x - 1)/(3x - 2)) - 5)^2 + 1(-1((-2x - 1)/(3x - 2)) - 5) + 1) - 1| and g(x) = 5(-5(-1sin(1πx - 1))^2 - 3(-1sin(1πx - 1)) + 1) - 3 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_667
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(3|((3(-4x + 5) + 1)/(2(-4x + 5) - 1))| + 2) - 3| + 3 and g(x) = -1cos(2π((1(-3x^2 - 4x - 5) - 1)/(-3(-3x^2 - 4x - 5) - 3)) + 3) + 1 from x = 1.3 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_668
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(2cos(2π(5(-1x^2 + 4x + 5)^2 - 2(-1x^2 + 4x + 5) + 3)) + 3) - 1)/(-2(2cos(2π(5(-1x^2 + 4x + 5)^2 - 2(-1x^2 + 4x + 5) + 3)) + 3) + 3) and g(x) = -5((-1(3e^(1x) + 1))/(1(3e^(1x) + 1) - 3))^2 + 2((-1(3e^(1x) + 1))/(1(3e^(1x) + 1) - 3)) + 5 between the vertical lines x = -1.7 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_669
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(1((3(1x + 4) + 1)/(-2(1x + 4)))^2 + 5((3(1x + 4) + 1)/(-2(1x + 4))) + 5)^2 - 1(1((3(1x + 4) + 1)/(-2(1x + 4)))^2 + 5((3(1x + 4) + 1)/(-2(1x + 4))) + 5), g(x) = 1|(2(-3e^(-2x) + 3)^2 + 2(-3e^(-2x) + 3) - 5) - 1| - 3, x = 0.2, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_670
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-2cos(1π(3(-2x^2 + 4)^2 - 5(-2x^2 + 4) - 1) - 2) - 3) + 4, g(x) = (1(1((-3x - 3)/(-3x - 1))^2 - 5((-3x - 3)/(-3x - 1)) - 4) + 2)/(-2(1((-3x - 3)/(-3x - 1))^2 - 5((-3x - 3)/(-3x - 1)) - 4) - 2), x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_671
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-4(-1(3|x| - 2) - 1)^2 - 2(-1(3|x| - 2) - 1) + 5)^2 - 3(-4(-1(3|x| - 2) - 1)^2 - 2(-1(3|x| - 2) - 1) + 5) - 3 and g(x) = -1(1(-3|x|)^2 - 5(-3|x|) - 3)^2 + 4(1(-3|x|)^2 - 5(-3|x|) - 3) - 3 from x = -0.6 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
52.0
|
math
|
train
|
math_algebra_func_area_level_3_3_672
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-1((-3((-3x + 2)/(-1x + 2)) - 1)/(-2((-3x + 2)/(-1x + 2))))^2 - 3((-3((-3x + 2)/(-1x + 2)) - 1)/(-2((-3x + 2)/(-1x + 2)))) - 3)^2 + 5(-1((-3((-3x + 2)/(-1x + 2)) - 1)/(-2((-3x + 2)/(-1x + 2))))^2 - 3((-3((-3x + 2)/(-1x + 2)) - 1)/(-2((-3x + 2)/(-1x + 2)))) - 3) + 4 and g(x) = 1|(-4(-3x + 1))| + 1 from x = 0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_3_3_673
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-5((-1(-1e^(-1x) + 1))/(2(-1e^(-1x) + 1) + 3))^2 - 2((-1(-1e^(-1x) + 1))/(2(-1e^(-1x) + 1) + 3)) - 1)^2 - 4(-5((-1(-1e^(-1x) + 1))/(2(-1e^(-1x) + 1) + 3))^2 - 2((-1(-1e^(-1x) + 1))/(2(-1e^(-1x) + 1) + 3)) - 1) + 5 and g(x) = -3|(-2cos(1π(2x - 5) + 2) - 3) + 3| + 2 from x = -4.1 to x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_3_3_674
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-4(-1sin(3π((-1x + 3)/(2x - 1)) + 2) + 3) - 4)| - 1 and g(x) = (-2(1|(-1|x + 1| + 3) + 2| - 2) + 3)/(-3(1|(-1|x + 1| + 3) + 2| - 2) + 2) from x = -3.3 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
78.7
|
math
|
train
|
math_algebra_func_area_level_3_3_675
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-5(-1((3x - 2)/(-3x))^2 + 4((3x - 2)/(-3x))) + 1)^2 + 5 and g(x) = (-2(5(2|x + 2|) - 4) + 2)/(2(5(2|x + 2|) - 4) - 1) from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_676
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-2|(2(2x - 1) - 2) + 1| + 2), g(x) = (1(-4(4x^2 + 2x - 5)^2 + 5(4x^2 + 2x - 5) + 1) + 3)/(-1(-4(4x^2 + 2x - 5)^2 + 5(4x^2 + 2x - 5) + 1) - 2), x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_677
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|((3(-2(2sin(1πx - 1) - 3) + 3) - 1)/(3(-2(2sin(1πx - 1) - 3) + 3)))| - 2, g(x) = 5(-1(-1|x + 3| - 2)^2 - 3(-1|x + 3| - 2) + 2) + 2, x = -4.9, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
61.3
|
math
|
train
|
math_algebra_func_area_level_3_3_678
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-4(-3cos(2π(-2x^2 + 3x + 5) + 2) + 3)^2 - 3(-3cos(2π(-2x^2 + 3x + 5) + 2) + 3) + 4) - 3)/(-2(-4(-3cos(2π(-2x^2 + 3x + 5) + 2) + 3)^2 - 3(-3cos(2π(-2x^2 + 3x + 5) + 2) + 3) + 4) - 1), g(x) = -1(-3sin(1π(-2|x - 2| - 2) - 3)), x = -4.2, and x = -4.1000000000000005. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_679
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-1|(-5(-2x + 2) + 3) - 1|) - 2)/(-1(-1|(-5(-2x + 2) + 3) - 1|) - 3) and g(x) = 1|(1sin(1π((-2x)/(2x - 3)) + 1) + 3) + 2| from x = 0.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_3_3_680
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2cos(3π(-2(-4(2x + 4)^2 + 2(2x + 4) - 5)^2 + 2(-4(2x + 4)^2 + 2(2x + 4) - 5) + 4) - 2) - 3, g(x) = -3(-1(-5x - 5)^2 + 3)^2 - 5(-1(-5x - 5)^2 + 3) + 2, x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_681
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(1((1((2x - 1)/(-2x - 1)))/(-2((2x - 1)/(-2x - 1)) - 2))^2 - 5((1((2x - 1)/(-2x - 1)))/(-2((2x - 1)/(-2x - 1)) - 2)) + 1) + 4 and g(x) = -3|(1cos(3π(1x + 2) - 3) - 2) - 3| between the vertical lines x = -4.8 and x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_682
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(5(-1(-2e^(-2x) - 1) - 5)^2 - 4) + 1 and g(x) = 1|(-4((1x + 3)/(-2x - 3))^2 + 1((1x + 3)/(-2x - 3)) + 5) - 1| + 2 between the vertical lines x = -0.5 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_3_3_683
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2(-1|((2x)/(-1x + 3)) + 1| + 1) + 1) + 3)/(-2(2(-1|((2x)/(-1x + 3)) + 1| + 1) + 1) - 1) and g(x) = -1((1((-1x)/(-3x - 1)) + 1)/(1((-1x)/(-3x - 1)) - 2))^2 + 1((1((-1x)/(-3x - 1)) + 1)/(1((-1x)/(-3x - 1)) - 2)) + 1 from x = -1.0 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.1
|
math
|
train
|
math_algebra_func_area_level_3_3_684
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|(1|((1((-2x + 1)/(-3x + 2)) + 2)/(-3((-2x + 1)/(-3x + 2)) - 3)) + 3| - 2) + 3| + 3 and g(x) = (2(-5(5x^2 + 5x) + 3) - 3)/(-1(-5(5x^2 + 5x) + 3) + 2) between the vertical lines x = -1.0 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.2
|
math
|
train
|
math_algebra_func_area_level_3_3_685
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-3cos(3π(-4((-3x)/(3x + 3))^2 + 2((-3x)/(3x + 3)) - 1)) + 2))/(3(-3cos(3π(-4((-3x)/(3x + 3))^2 + 2((-3x)/(3x + 3)) - 1)) + 2)) and g(x) = -4(-3((2x - 3)/(2x - 1)) - 2)^2 + 4(-3((2x - 3)/(2x - 1)) - 2) + 2 from x = 1.0 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_686
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3((-3(2cos(3π(3|x - 1|) - 1) + 1) + 2)/(3(2cos(3π(3|x - 1|) - 1) + 1) - 1)) - 1)/(1((-3(2cos(3π(3|x - 1|) - 1) + 1) + 2)/(3(2cos(3π(3|x - 1|) - 1) + 1) - 1)) + 1), g(x) = (3((-1(4x + 5))/(-1(4x + 5) + 3)) + 3)/(1((-1(4x + 5))/(-1(4x + 5) + 3))), x = 1.1, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_687
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(5(-1|(1e^(-2x) + 2)|) + 5) + 3)/(2(5(-1|(1e^(-2x) + 2)|) + 5) + 3) and g(x) = -2|(-5(-2x^2 + 2x + 3)) + 1| + 3 from x = -0.8 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_688
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(2((2(-2x - 5))/(-2(-2x - 5))) - 3) + 5 and g(x) = -1((-3(2cos(3πx + 1)) + 2)/(1(2cos(3πx + 1)) + 1)) - 3 between the vertical lines x = 2.8 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_3_3_689
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-3|(2(-1|x + 2| - 3) + 5) + 3| + 1) + 2| - 2 and g(x) = (-2(-1(-3x^2 - 2x + 2) - 2) + 3)/(-1(-1(-3x^2 - 2x + 2) - 2) + 3) between the vertical lines x = -1.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
46.3
|
math
|
train
|
math_algebra_func_area_level_3_3_690
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(-1cos(1π(-5(-3x)) - 2)) + 1| + 3 and g(x) = (3(1(2|x| - 2)^2 + 3(2|x| - 2) + 2) + 2)/(-1(1(2|x| - 2)^2 + 3(2|x| - 2) + 2) + 2) 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_691
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2sin(3π(4(2(-1x^2 - 4x - 5) - 4) - 4) + 3) + 3 and g(x) = -1((1(2x^2 - 5x - 3))/(1(2x^2 - 5x - 3) - 3))^2 + 4((1(2x^2 - 5x - 3))/(1(2x^2 - 5x - 3) - 3)) + 1 from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_692
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-1sin(2π(-2|(1x - 4) - 1|) + 3) + 2))/(-2(-1sin(2π(-2|(1x - 4) - 1|) + 3) + 2) - 2), g(x) = -1(1|(-2x) - 2| - 3) + 2, x = -3.6, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.2
|
math
|
train
|
math_algebra_func_area_level_3_3_693
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-2cos(2π(3|(-1|x - 1| + 1) - 3| - 3) + 1) - 3) + 4 and g(x) = 3((1(1x - 5) - 2)/(2(1x - 5) + 2))^2 + 1((1(1x - 5) - 2)/(2(1x - 5) + 2)) from x = 2.7 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_694
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-1(-1(4x^2 + 2x - 5) - 3) - 4) - 1)/(-2(-1(-1(4x^2 + 2x - 5) - 3) - 4) + 3), g(x) = 2(-2cos(2π((-2x - 3)/(-2x - 1)) - 1) + 1) - 3, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_695
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(2(-1|(5x^2 - 5x) + 3| + 3) - 4)^2 - 5(2(-1|(5x^2 - 5x) + 3| + 3) - 4) + 2 and g(x) = -5(2|(2x^2 - 4) - 2| + 1) - 5 from x = -0.5 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
108.0
|
math
|
train
|
math_algebra_func_area_level_3_3_696
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-1cos(1π((-2((-3x - 1)/(-2x)) + 2)/(-1((-3x - 1)/(-2x)) + 2))) + 3) - 1 and g(x) = 3|(-1e^(2((-2x + 2)/(3x - 2))) + 1) + 1| + 3 between the vertical lines x = 0.9 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_697
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(1(-2|((-3x - 2)/(2x + 3)) + 1| + 3)^2 - 3(-2|((-3x - 2)/(2x + 3)) + 1| + 3) - 5) + 2| and g(x) = -2e^(-2(-4((-2x - 1)/(-2x + 3))^2 + 1((-2x - 1)/(-2x + 3)) + 5)) + 2 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_698
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2cos(1π(-4(4(-1|x - 1| - 1)^2 - 4(-1|x - 1| - 1)) + 1)) + 2 and g(x) = (3(1(1x - 2)^2 - 5(1x - 2) - 3) - 1)/(-2(1(1x - 2)^2 - 5(1x - 2) - 3) + 3) between the vertical lines x = 1.3 and x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_699
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((1(3(-3cos(1πx + 3)) + 3) - 3)/(2(3(-3cos(1πx + 3)) + 3) - 1)) - 2 and g(x) = (-3(-1(-3e^(2x) - 3) - 1) - 2)/(-3(-1(-3e^(2x) - 3) - 1) + 2) from x = -4.5 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.6
|
math
|
train
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.