messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((2(-2x) - 3)/(3(-2x)))^2 + 3((2(-2x) - 3)/(3(-2x))) - 2, g(x) = -4(2cos(3πx + 1))^2 + 5(2cos(3πx + 1)) + 5, x = -4.8, and x = -4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(2π(-2|(3x - 4) - 2| + 2) + 2) + 2 and g(x) = -5((-2x + 2)/(2x - 1))^2 - 1((-2x + 2)/(2x - 1)) + 4 between the vertical lines x = 3.2 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2|(-4x^2 + 4x + 3) + 3| + 3) + 2 and g(x) = 2(-3x - 1) - 2 between the vertical lines x = 1.5 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(2((-2x)/(2x + 2)) - 1)^2 + 5(2((-2x)/(2x + 2)) - 1) + 2 and g(x) = 3(-5x^2 + 2x + 3) - 4 from x = -0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(2sin(3π(-2|x + 3| + 3) + 3) + 1) - 3)/(1(2sin(3π(-2|x + 3| + 3) + 3) + 1) - 2) and g(x) = 1(1cos(3πx - 3) + 1)^2 + 5(1cos(3πx - 3) + 1) + 1 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent th... | 4.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(1|(-1sin(3πx + 3) - 2) + 2| + 3) + 5, g(x) = -1(-4x + 1) + 1, x = 4.4, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(1π(1|((-1x - 2)/(-1x + 3)) + 2| - 3) + 3) - 2 and g(x) = 1|(-3|x - 1| + 2) + 1| - 2 from x = 2.6 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2(-3sin(2πx - 2) - 2) - 2) - 3)/(2(-2(-3sin(2πx - 2) - 2) - 2) + 2) and g(x) = 3|(-1e^(1x) + 2) + 3| - 2 between the vertical lines x = 0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1e^(1(-3((2x - 1)/(-3x - 2))^2 - 4((2x - 1)/(-3x - 2)) + 4)) - 1 and g(x) = (-2(5x^2 + 5x - 5) - 1)/(-3(5x^2 + 5x - 5)) from x = -1.3 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 1.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2(2|x + 2| - 1) + 1) - 4 and g(x) = 4(-2x^2 - 3x + 3)^2 + 4 between the vertical lines x = 0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(1|(2x - 5)| - 2) - 3)/(-2(1|(2x - 5)| - 2) + 3) and g(x) = 2sin(1π(2x - 2) + 2) + 2 from x = -3.8 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2|(2|x + 1| - 3) - 3| - 3)^2 + 5(2|(2|x + 1| - 3) - 3| - 3) - 5 and g(x) = 3cos(3π(1x - 1) + 2) + 2 between the vertical lines x = -3.8 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 4.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(2|(3sin(2πx + 3) - 2) + 1|) - 1)/(-1(2|(3sin(2πx + 3) - 2) + 1|) + 2), g(x) = -1(3e^(2x) - 3) + 3, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 2.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-2(-1|x + 3| + 1) + 2) + 3)/(-1(-2(-1|x + 3| + 1) + 2) + 2) and g(x) = (3(-4x^2 + 4x + 3) + 1)/(1(-4x^2 + 4x + 3) - 2) from x = -2.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 19.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3((-1(4x^2 + 5x - 3) - 2)/(-1(4x^2 + 5x - 3) + 3)) - 2)/(-1((-1(4x^2 + 5x - 3) - 2)/(-1(4x^2 + 5x - 3) + 3)) - 1), g(x) = (3(-3x^2 - 4x - 3) - 3)/(2(-3x^2 - 4x - 3) - 1), x = -1.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPrese... | 1.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1((-3(-3e^(1x) + 2) + 1)/(-2(-3e^(1x) + 2) - 2)) - 2)/(-2((-3(-3e^(1x) + 2) + 1)/(-2(-3e^(1x) + 2) - 2)) + 3), g(x) = -2sin(1π(-1|x - 1| - 1) - 3) + 1, x = -2.7, and x = -2.4. Round your answer to 1 decimal place.\n\nPresent the answer in L... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(1sin(3π(2x^2 + 2x) - 1)) + 2)/(1(1sin(3π(2x^2 + 2x) - 1)) + 1), g(x) = 1(-3cos(1πx + 2) - 2)^2 - 3(-3cos(1πx + 2) - 2) - 5, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 40.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(3sin(3π((-2x - 3)/(3x - 1)) - 1) + 1) + 3)/(-3(3sin(3π((-2x - 3)/(3x - 1)) - 1) + 1) + 1), g(x) = (3(1|x - 3|) + 1)/(-3(1|x - 3|) - 1), x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((-3(-3|x + 2| + 3) + 3)/(-2(-3|x + 2| + 3) + 3)) + 1)/(-3((-3(-3|x + 2| + 3) + 3)/(-2(-3|x + 2| + 3) + 3))), g(x) = -1|(3x - 5) + 1| + 2, x = -1.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format:... | 6.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3(-1|x - 1| + 1)^2 - 1(-1|x - 1| + 1) + 1)^2 + 4(-3(-1|x - 1| + 1)^2 - 1(-1|x - 1| + 1) + 1) + 5 and g(x) = 1((2x - 3)/(-3x))^2 - 3((2x - 3)/(-3x)) + 2 between the vertical lines x = -1.2 and x = 0.2. Round to 1 decimal place.\n\... | -6.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((-1(-3|x + 1| + 3) - 2)/(-3(-3|x + 1| + 3) + 2)), g(x) = -1cos(3π(-2x^2 - 3)) + 3, x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(4x + 1))/(-2(4x + 1) - 3))^2 - 3 and g(x) = -2(2e^(-1x) - 1)^2 - 4(2e^(-1x) - 1) - 2 between the vertical lines x = -0.8 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -10.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((3(-5x^2 + 4) + 1)/(-2(-5x^2 + 4) - 1)) + 2| - 2 and g(x) = -2sin(3π(-5x^2 + 4x - 4) - 1) - 1 between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(3cos(2π(-1x^2 - 5x + 3) + 1) - 2) - 2, g(x) = 2|(4x^2 + 3x - 3) - 3| - 1, x = -1.7, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(1sin(3π((-2x - 3)/(-2x)) + 3) + 2) - 4 and g(x) = -1e^(-1(-5x^2 + 5x + 4)) from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-5((-1x + 3)/(-1x - 2))^2 + 5((-1x + 3)/(-1x - 2)) - 4) + 1 and g(x) = 4(-1cos(1πx + 1) + 3)^2 + 1(-1cos(1πx + 1) + 3) - 1 between the vertical lines x = 2.0 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex f... | 36.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(4((-2x - 2)/(-3x + 1))^2 + 2((-2x - 2)/(-3x + 1)) - 4) + 5, g(x) = -1(-2|x - 3| - 2) + 4, x = -2.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3((1(2|x + 3| + 2) + 1)/(1(2|x + 3| + 2) - 3)))/(1((1(2|x + 3| + 2) + 1)/(1(2|x + 3| + 2) - 3))), g(x) = 1e^(-1(-3|x + 1| + 1)), x = -1.7, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 2.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-1(1|x + 2|) + 4)^2 - 2(-1(1|x + 2|) + 4) - 2, g(x) = 3sin(3π(-3x - 2) - 1) - 1, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(1π((3(1x^2 + 1x + 1) + 3)/(-1(1x^2 + 1x + 1))) + 2) and g(x) = 3|(-2|x - 3| + 1) + 2| - 3 between the vertical lines x = 0.9 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(3sin(3π((3x + 3)/(1x)) - 2)) + 3)/(-1(3sin(3π((3x + 3)/(1x)) - 2)) + 3) and g(x) = 1|(1x^2 - 1x - 2) + 2| - 2 from x = -4.5 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 23.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(2|(4x - 3) - 3| - 3) + 2)/(-2(2|(4x - 3) - 3| - 3) - 1), g(x) = -2(-4x - 3) - 1, x = 1.2, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(2|(-2|x + 1| + 1) - 2| - 2) - 1, g(x) = 1(2sin(2πx + 1) - 1)^2 + 4(2sin(2πx + 1) - 1) - 1, x = -1.8, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2π(-1(4x^2 - 4x) + 3) - 1) - 2 and g(x) = 4(-1cos(1πx - 1) + 1)^2 - 5(-1cos(1πx - 1) + 1) - 4 between the vertical lines x = -5.0 and x = -4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2|(2x^2 + 5x + 2) - 2| + 3) + 1 and g(x) = (1(1e^(1x) + 1) + 2)/(1(1e^(1x) + 1) + 3) between the vertical lines x = -0.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 2.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(5(3x)^2 + 4(3x) + 2)^2 + 3 and g(x) = -2(4x^2 - 1x - 2)^2 + 1(4x^2 - 1x - 2) - 1 from x = -0.3 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(3sin(2π(-3x^2 + 2x + 1) + 2))^2 - 1(3sin(2π(-3x^2 + 2x + 1) + 2)) and g(x) = (-1((1x + 3)/(1x + 2)))/(2((1x + 3)/(1x + 2)) - 3) from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3((-3((2x + 1)/(-1x - 1)) - 2)/(1((2x + 1)/(-1x - 1))))^2 - 5((-3((2x + 1)/(-1x - 1)) - 2)/(1((2x + 1)/(-1x - 1)))) + 2, g(x) = 1cos(2π((1x - 2)/(-2x + 3))) + 1, x = -0.3, and x = -0.19999999999999998. Round your answer to 1 decimal place.\n... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π(3(-3x^2 + 1x) - 2)) + 2 and g(x) = 2(-2x^2 - 1x + 1) - 1 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(1π(5(2|x - 3| + 3)^2 + 5(2|x - 3| + 3) - 3) + 3), g(x) = 1(3e^(2x))^2 + 2(3e^(2x)) - 5, x = -0.4, and x = -0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3sin(1π(-2|x - 2|) + 1) - 3)^2 - 2(-3sin(1π(-2|x - 2|) + 1) - 3) + 2 and g(x) = -2(1x^2 + 5x - 4)^2 - 2(1x^2 + 5x - 4) + 2 between the vertical lines x = 0.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex ... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3π(-3|(1|x + 3| - 2) - 3|) - 2) + 3 and g(x) = (2(-2x - 4) + 2)/(1(-2x - 4)) between the vertical lines x = -2.9 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(5(-5x^2 + 3x + 3)^2 + 4(-5x^2 + 3x + 3)) + 1)/(-2(5(-5x^2 + 3x + 3)^2 + 4(-5x^2 + 3x + 3)) - 3) and g(x) = -2sin(3π(2x^2 + 5x) + 3) - 1 from x = -2.1 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(3|(-5x^2 - 1x + 3) + 3| + 3) - 3)/(1(3|(-5x^2 - 1x + 3) + 3| + 3) - 2) and g(x) = -2(1cos(2πx + 2)) + 3 from x = 0.9 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((1(-2|x - 1| + 3) + 2)/(-2(-2|x - 1| + 3) - 1)) - 2, g(x) = -2cos(3π(3x^2 - 3x + 2) - 2) + 3, x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((1((1x - 1)/(3x - 2)) - 1)/(-2((1x - 1)/(3x - 2)) + 3)) + 1| + 2 and g(x) = (2(3x + 3) + 2)/(-3(3x + 3) - 1) between the vertical lines x = 0.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxe... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-5(4x^2 - 4x)^2 + 3(4x^2 - 4x) + 4) + 5 and g(x) = -5((1x - 3)/(-2x - 1)) + 2 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": "us... | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1|(2x - 1) - 1| + 3) and g(x) = 2(-3x^2 - 2x + 3) - 3 between the vertical lines x = -0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-3(1cos(1πx - 3)) + 2)/(-1(1cos(1πx - 3)) + 3)) - 1)/(1((-3(1cos(1πx - 3)) + 2)/(-1(1cos(1πx - 3)) + 3))) and g(x) = 1(2x^2 - 1x - 4)^2 + 1(2x^2 - 1x - 4) - 3 between the vertical lines x = 0.7 and x = 1.1. Round to 1 decimal p... | 1.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1(-1x^2 - 1x))^2 - 3(1(-1x^2 - 1x)) - 4 and g(x) = 5(-2|x + 1| + 3)^2 + 2(-2|x + 1| + 3) + 1 between the vertical lines x = -2.0 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 61.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-1(-4x^2 - 5x) + 3)/(3(-4x^2 - 5x) + 1)) + 4 and g(x) = -2sin(2π(-1x^2 - 3x - 5) - 1) - 3 between the vertical lines x = -1.3 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 7.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(2|(-2e^(1x) + 3)| - 2) - 1)/(3(2|(-2e^(1x) + 3)| - 2) + 3), g(x) = 2e^(-2((1x - 2)/(-1x + 2))) - 2, x = 0.2, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 9.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(4x^2 + 4x) - 3)/(3(4x^2 + 4x) - 1)) + 1 and g(x) = -5(-2|x - 1| - 1)^2 - 3(-2|x - 1| - 1) + 5 between the vertical lines x = 0.1 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 7.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(1(-1e^(2x)) + 1)^2 + 3(1(-1e^(2x)) + 1) - 4 and g(x) = 3e^(-1(-3x + 4)) - 2 from x = -0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2((1(-3x^2 + 1x + 1))/(3(-3x^2 + 1x + 1) - 2)) - 2)/(-2((1(-3x^2 + 1x + 1))/(3(-3x^2 + 1x + 1) - 2))) and g(x) = -3(-1cos(3πx - 3))^2 - 1(-1cos(3πx - 3)) + 2 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1((2((-1x - 3)/(2x - 1)) + 2)/(-3((-1x - 3)/(2x - 1)) - 2)) - 3)/(-3((2((-1x - 3)/(2x - 1)) + 2)/(-3((-1x - 3)/(2x - 1)) - 2)) - 3) and g(x) = 1(3x^2 + 2x - 5)^2 + 4(3x^2 + 2x - 5) - 5 from x = -2.0 to x = 1.2. Round to 1 decimal place.\n\n... | 31.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(2(-4x^2 + 1x) - 5) + 2| - 2 and g(x) = -2e^(1(-3|x + 2| - 1)) + 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"
}
] | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2(3sin(2πx + 2) - 2) + 1)^2 - 2(-2(3sin(2πx + 2) - 2) + 1) - 5 and g(x) = -1((2x + 3)/(-1x + 2)) - 2 between the vertical lines x = 1.0 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 89.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((-2(-3sin(2πx + 3) - 1))/(-2(-3sin(2πx + 3) - 1) + 3)) + 2| - 3 and g(x) = -5(-1x + 2) - 4 from x = 2.4 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((3(4x^2 - 2x - 5) + 2)/(-3(4x^2 - 2x - 5) - 3)) and g(x) = 3(1x + 4) - 2 between the vertical lines x = -5.0 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 25.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(3π((-1(-4x - 2))/(-2(-4x - 2) + 3)) + 2) + 2, g(x) = 1|(3x + 5) + 2| - 1, x = -1.5, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(-1(1x + 2) + 3) + 2| - 1 and g(x) = 2e^(1(2|x + 3|)) - 1 from x = -4.0 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((2(-5x^2 - 3x + 4) - 1)/(3(-5x^2 - 3x + 4) + 1))| + 1 and g(x) = 2sin(2π((1x - 2)/(-1x - 1)) - 3) 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 ans... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π(2(-4x^2 + 2x + 5)^2 + 3(-4x^2 + 2x + 5) + 1) + 3) - 2 and g(x) = 2(-1x^2)^2 + 5(-1x^2) + 2 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2cos(2π((-3x - 2)/(2x - 1)) + 2) - 1)^2 - 2 and g(x) = -2|(1sin(1πx + 3) + 1)| - 2 between the vertical lines x = -1.5 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 6.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(3|(-1x^2 + 1x + 4) + 1| - 2) + 1)/(2(3|(-1x^2 + 1x + 4) + 1| - 2) - 1) and g(x) = -5(-5x - 4) - 1 from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3(-2cos(3πx - 1) + 3) + 5) - 3)/(-3(3(-2cos(3πx - 1) + 3) + 5) - 1) and g(x) = 2(-2x - 1)^2 + 1 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(-1cos(2π(-1|x + 1| + 3) - 1)) - 5, g(x) = -1sin(1π((-1x + 2)/(-1x + 3)) + 2) - 2, x = 2.9, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-2sin(3π(1|x| - 3) - 1))^2 + 5(-2sin(3π(1|x| - 3) - 1)) - 4, g(x) = (2(-4x^2 - 2x - 2) - 2)/(2(-4x^2 - 2x - 2) - 1), x = 2.8, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(3(-3x^2 - 5x + 4) + 5) + 2)/(-1(3(-3x^2 - 5x + 4) + 5)), g(x) = 3(1x^2 + 3x - 4) - 3, x = -2.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(1sin(3πx - 3)) + 1| + 2) + 1)/(-3(-1|(1sin(3πx - 3)) + 1| + 2) - 1), g(x) = -3sin(1π((1x + 2)/(-3x - 3)) - 3) + 1, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-2(3sin(3πx + 3) - 2) - 1) - 1| - 1 and g(x) = -1e^(1(-3x - 1)) between the vertical lines x = -1.2 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((1(5x + 3) + 2)/(-2(5x + 3) + 1))| + 3 and g(x) = -3(1|x - 1| - 1)^2 - 2(1|x - 1| - 1) + 3 between the vertical lines x = -0.6 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 20.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(1(3x + 1)^2 - 3(3x + 1) - 4) + 1)/(-3(1(3x + 1)^2 - 3(3x + 1) - 4) + 4) and g(x) = 3|(-4x + 4) - 3| - 1 from x = 0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1(-2|x + 1| + 1)^2 - 4(-2|x + 1| + 1) - 2)^2 - 5(1(-2|x + 1| + 1)^2 - 4(-2|x + 1| + 1) - 2) and g(x) = 5(-3cos(3πx) - 2)^2 - 4 between the vertical lines x = -0.5 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in L... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(2(3cos(3πx + 3) + 3) - 5) + 5 and g(x) = -3sin(3π((-2x + 1)/(-3x)) + 3) + 1 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"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1cos(3π(-2|x + 3| - 3)) - 2) + 3| + 3 and g(x) = (3(4x^2 - 1x + 5) - 3)/(-3(4x^2 - 1x + 5) - 2) 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... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1(-3sin(1πx - 3) + 2) - 4) + 3| - 2 and g(x) = -3(1x^2 + 4x - 1)^2 - 5(1x^2 + 4x - 1) + 2 between the vertical lines x = -4.4 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 9.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(4(-2sin(1πx + 3) - 2)^2 + 3(-2sin(1πx + 3) - 2) - 4) - 1| - 2 and g(x) = (-1(-5x^2 - 1x + 3) - 3)/(-1(-5x^2 - 1x + 3) - 1) between the vertical lines x = -3.1 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(3(2|x - 1|)^2 - 4(2|x - 1|) + 5) - 3| and g(x) = -3cos(2π(1|x - 1| + 2) + 1) + 2 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"
}
] | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1sin(3π(1x^2 + 3) - 2) + 1) - 3| + 1 and g(x) = -3|((2x)/(2x - 1)) + 1| - 1 between the vertical lines x = 2.2 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-1sin(1π((-2x + 2)/(1x))) - 2), g(x) = -3|(-5x - 3) - 2|, x = -0.7, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(3e^(-2x) - 3) - 1) - 2| and g(x) = -1(1|x - 2| - 3)^2 - 4(1|x - 2| - 3) - 5 between the vertical lines x = 0.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((-2((-3x + 1)/(1x)))/(-2((-3x + 1)/(1x)) + 3))^2 - 1((-2((-3x + 1)/(1x)))/(-2((-3x + 1)/(1x)) + 3)) + 2, g(x) = 2(1e^(2x))^2 - 4(1e^(2x)) - 4, x = 0.2, and x = 0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answ... | -0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1|(-2|x + 2| - 2)| + 3) - 1 and g(x) = (-1(3|x - 3| - 3) - 2)/(-1(3|x - 3| - 3) + 3) between the vertical lines x = -1.2 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 19.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((3(-1x + 3) - 3)/(-2(-1x + 3)))^2 + 2((3(-1x + 3) - 3)/(-2(-1x + 3))) - 5 and g(x) = (2(-2sin(2πx - 1) - 2) + 3)/(-2(-2sin(2πx - 1) - 2) - 1) between the vertical lines x = 1.0 and x = 1.8. Round to 1 decimal place.\n\nPresent th... | 8.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-1((3x + 3)/(3x + 2)) - 2)/(-1((3x + 3)/(3x + 2)) - 1)) - 2| + 2 and g(x) = -3sin(3π((-3x + 3)/(-1x - 1)) - 3) - 3 between the vertical lines x = -0.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex forma... | 4.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((2(-1x^2 + 3x - 1) - 2)/(-1(-1x^2 + 3x - 1) + 3))^2 - 4((2(-1x^2 + 3x - 1) - 2)/(-1(-1x^2 + 3x - 1) + 3)) - 4 and g(x) = (3(2|x + 1| + 2) + 1)/(1(2|x + 1| + 2) + 2) from x = -0.3 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer ... | 15.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-3|x + 2| + 3) + 2| - 2) + 1)/(-1(-2|(-3|x + 2| + 3) + 2| - 2) + 2) and g(x) = 2cos(3π(2|x + 2| + 2) - 1) + 2 between the vertical lines x = -3.3 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(2|(2x + 2) + 1| - 1) - 1)/(1(2|(2x + 2) + 1| - 1)), g(x) = 1(-5x - 1) - 1, x = -1.7, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1(2|x + 2| + 1) - 5) + 3)/(-2(1(2|x + 2| + 1) - 5) + 1) and g(x) = (-1(-2sin(2πx + 1) - 2) - 1)/(2(-2sin(2πx + 1) - 2) + 3) between the vertical lines x = -3.6 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaT... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-2|(2x^2 + 3x - 4)| + 2) + 2)/(-3(-2|(2x^2 + 3x - 4)| + 2)), g(x) = -3((-2x + 1)/(-2x - 2))^2 + 5((-2x + 1)/(-2x - 2)) - 1, x = -2.5, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 2.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((-2(1cos(1πx - 2) + 1) - 1)/(2(1cos(1πx - 2) + 1) - 1)) - 2, g(x) = (1(-3x + 2) - 2)/(1(-3x + 2)), x = 1.1, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 25.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(1(-5x - 3) - 5)^2 + 2(1(-5x - 3) - 5) - 3 and g(x) = -1cos(3π(5x + 5) + 1) from x = -1.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π(-5(1x^2 - 2x - 4)) + 1) + 1 and g(x) = 4(-2sin(1πx + 2) + 3)^2 - 5 between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4(3sin(1πx - 3) - 2) + 2) - 1 and g(x) = (-2(1e^(-1x) + 3) + 2)/(2(1e^(-1x) + 3)) 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}",
"role"... | 28.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3((2(4x + 5) - 1)/(1(4x + 5))) - 3)/(-2((2(4x + 5) - 1)/(1(4x + 5))) - 2), g(x) = 3(3sin(3πx + 3) + 1) + 2, x = -1.2, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(2|(4x^2 - 1x - 4)| - 1) + 2, g(x) = -1(1|x + 1|) + 4, x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(1|(-1cos(2πx - 1) - 3)| + 1) + 5, g(x) = (-3(-2|x|) - 3)/(-2(-2|x|) - 1), 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"
}
] | 23.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(1|((-1x + 2)/(2x + 1)) + 2| - 1))/(1(1|((-1x + 2)/(2x + 1)) + 2| - 1) - 3) and g(x) = (-1(-5x^2 - 1x - 5))/(-1(-5x^2 - 1x - 5) - 3) from x = -0.8 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 23.1 | MATH |
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