messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((2((3(-1x^2 + 2x - 2) - 3)/(-2(-1x^2 + 2x - 2) - 3)) + 1)/(3((3(-1x^2 + 2x - 2) - 3)/(-2(-1x^2 + 2x - 2) - 3)) - 2))^2 - 2((2((3(-1x^2 + 2x - 2) - 3)/(-2(-1x^2 + 2x - 2) - 3)) + 1)/(3((3(-1x^2 + 2x - 2) - 3)/(-2(-1x^2 + 2x - 2) - 3)) - 2)... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3π(1(-5(4x + 4)^2 + 4(4x + 4) - 4)^2 + 5(-5(4x + 4)^2 + 4(4x + 4) - 4) + 4) - 1) - 1 and g(x) = (1(2|(-2e^(1x) - 2) - 2| - 1) + 3)/(-3(2|(-2e^(1x) - 2) - 2| - 1) - 3) between the vertical lines x = 0.4 and x = 0.5. Round to 1 d... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1e^(-2(-5(3x^2 + 2x - 1)^2 - 4(3x^2 + 2x - 1) + 5)) - 3) + 5 and g(x) = (2(-3|(3x^2 + 1x + 3) + 3| - 3) - 2)/(1(-3|(3x^2 + 1x + 3) + 3| - 3) - 3) between the vertical lines x = -1.2 and x = 0.5. Round to 1 decimal place.\n\nPrese... | 12.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(5(3((2x)/(2x - 1))^2 + 2((2x)/(2x - 1)) - 3)^2 - 4(3((2x)/(2x - 1))^2 + 2((2x)/(2x - 1)) - 3) - 1) + 2)/(2(5(3((2x)/(2x - 1))^2 + 2((2x)/(2x - 1)) - 3)^2 - 4(3((2x)/(2x - 1))^2 + 2((2x)/(2x - 1)) - 3) - 1) + 1) and g(x) = -3|(-2(5x^2 - 1x... | 79.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1((-1(3|x - 3| - 2) - 3)/(1(3|x - 3| - 2) - 3)) + 4) + 1, g(x) = 2|((3(-3|x - 1| + 2) + 2)/(-2(-3|x - 1| + 2) - 3)) - 3| - 1, x = 2.3, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 13.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(2sin(2π((3x)/(1x + 1)) - 1) - 3) - 2)/(-1(2sin(2π((3x)/(1x + 1)) - 1) - 3) - 1)) and g(x) = 2|((-2(3x^2 - 5x + 3) - 3)/(-2(3x^2 - 5x + 3) + 3)) - 1| + 3 between the vertical lines x = -1.2 and x = -1.0999999999999999. Round to... | 75.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(1(-4x^2 - 1x - 2) - 2)^2 + 5(1(-4x^2 - 1x - 2) - 2) + 4))/(1(-1(1(-4x^2 - 1x - 2) - 2)^2 + 5(1(-4x^2 - 1x - 2) - 2) + 4) + 1) and g(x) = -2|(-1|(-1|x - 2|) + 1| - 1) + 3| + 2 from x = 0.5 to x = 1.5. Round to 1 decimal place.\n\nPrese... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-2e^(-2(2(1|x + 1|)^2 + 2(1|x + 1|))) - 1) - 4 and g(x) = -1|(-2cos(1π((1x + 2)/(2x - 3)) + 3) + 1) + 3| - 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{... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-1(4(2x^2 + 2x - 1) + 1)^2 + 4(4(2x^2 + 2x - 1) + 1) + 4) + 4, g(x) = 3(-3sin(1π(-1x + 5) - 2) - 2) - 4, 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... | 7.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((1((1(-1x^2 + 1x - 1) + 1)/(2(-1x^2 + 1x - 1) - 3)) - 3)/(1((1(-1x^2 + 1x - 1) + 1)/(2(-1x^2 + 1x - 1) - 3)) + 1)) - 3)/(-3((1((1(-1x^2 + 1x - 1) + 1)/(2(-1x^2 + 1x - 1) - 3)) - 3)/(1((1(-1x^2 + 1x - 1) + 1)/(2(-1x^2 + 1x - 1) - 3)) + 1)... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2((1(-2(2sin(2πx + 3) - 3) - 1) - 2)/(-1(-2(2sin(2πx + 3) - 3) - 1))) - 4, g(x) = -4(-3e^(2((2x - 2)/(-1x + 2))))^2 - 2(-3e^(2((2x - 2)/(-1x + 2)))) - 4, x = 3.9, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in La... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(1(4((3x - 2)/(2x - 1))^2 + 1((3x - 2)/(2x - 1)) - 2) - 5) + 2)/(2(1(4((3x - 2)/(2x - 1))^2 + 1((3x - 2)/(2x - 1)) - 2) - 5)), g(x) = 3cos(2π(-1|(3x + 4) - 3| - 3) - 3) + 1, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\n... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(3cos(2π(1(-1x^2 + 4)^2 + 5(-1x^2 + 4) - 4) + 3) + 2) - 1| and g(x) = 5(1|(3|x - 1| - 3) + 3| - 2) + 5 from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-3(-1|(-3x^2 - 4x - 1) - 2|)^2 - 2(-1|(-3x^2 - 4x - 1) - 2|) - 3) + 1)/(-1(-3(-1|(-3x^2 - 4x - 1) - 2|)^2 - 2(-1|(-3x^2 - 4x - 1) - 2|) - 3) + 2), g(x) = (-1(-1|(3|x| + 3) - 2| + 3) + 3)/(-3(-1|(3|x| + 3) - 2| + 3)), x = -0.5, and x = 0.6... | 2.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1|(-1(-3e^(1x) - 3)^2 + 3(-3e^(1x) - 3) - 4) - 2| + 2) - 1)/(1(1|(-1(-3e^(1x) - 3)^2 + 3(-3e^(1x) - 3) - 4) - 2| + 2)) and g(x) = 4(1|(2x - 5) - 1| - 1) - 2 between the vertical lines x = 2.0 and x = 4.0. Round to 1 decimal place... | 8.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((3(1|(2x + 3)| - 3) + 2)/(-3(1|(2x + 3)| - 3) + 4))^2 + 5((3(1|(2x + 3)| - 3) + 2)/(-3(1|(2x + 3)| - 3) + 4)) + 3 and g(x) = (1(2cos(3π(1x^2 + 2) - 3) - 1) + 2)/(-1(2cos(3π(1x^2 + 2) - 3) - 1) - 1) between the vertical lines x = -... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(3|((-1(-3x + 5) + 3)/(-3(-3x + 5) - 1)) - 1| - 1) + 3)/(-1(3|((-1(-3x + 5) + 3)/(-3(-3x + 5) - 1)) - 1| - 1) + 2) and g(x) = -3(3cos(3π(4x + 5) - 1) - 3)^2 - 1(3cos(3π(4x + 5) - 1) - 3) - 1 from x = -1.4 to x = -1.2. Round to 1 decimal p... | 6.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-2|(-5(-3sin(1πx + 2) + 2)^2 - 4(-3sin(1πx + 2) + 2) + 3)|)^2 - 3 and g(x) = 1|((-3(4x^2 + 4x - 4) - 2)/(-2(4x^2 + 4x - 4) + 3)) + 3| + 2 from x = -3.8 to x = -3.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex fo... | 35.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|((-2((-1x - 3)/(1x + 2)) - 1)/(-1((-1x - 3)/(1x + 2)) + 2)) - 2|) + 4 and g(x) = (2(2|(2cos(2πx + 3) - 2) - 2| + 3) + 2)/(1(2|(2cos(2πx + 3) - 2) - 2| + 3) - 3) between the vertical lines x = -2.0 and x = -1.9. Round to 1 decim... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1|((-2(-1x^2 - 4x - 5))/(2(-1x^2 - 4x - 5) + 3))| - 3) - 3| and g(x) = -2(-3e^(2(-3x^2 - 1x + 1)) - 1)^2 + 4(-3e^(2(-3x^2 - 1x + 1)) - 1) + 1 between the vertical lines x = -2.8 and x = -2.6. Round to 1 decimal place.\n\nPresent... | 54.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((1((-1((-2x + 3)/(2x - 1)))/(1((-2x + 3)/(2x - 1)) - 3)) - 2)/(2((-1((-2x + 3)/(2x - 1)))/(1((-2x + 3)/(2x - 1)) - 3))))^2 + 2((1((-1((-2x + 3)/(2x - 1)))/(1((-2x + 3)/(2x - 1)) - 3)) - 2)/(2((-1((-2x + 3)/(2x - 1)))/(1((-2x + 3)/(2x - 1))... | 18.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-2(2(-4x^2 + 1x + 3) - 2) + 4) - 3)/(-3(-2(2(-4x^2 + 1x + 3) - 2) + 4) - 1), g(x) = (2((3(-1|x - 1| - 3) - 3)/(-1(-1|x - 1| - 3) - 1)) - 1)/(3((3(-1|x - 1| - 3) - 3)/(-1(-1|x - 1| - 3) - 1))), x = -0.5, and x = 0.8. Round your answer to ... | 3.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1|(2|((-1x + 1)/(-1x - 3)) - 3| + 1) - 3| + 1) + 4, g(x) = 1sin(3π((-1((-1x + 3)/(-1x + 2)) + 3)/(-2((-1x + 3)/(-1x + 2)) - 2))) + 1, x = -4.8, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 2.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(1|(1cos(2π((2x - 2)/(1x - 2)) + 2))| - 1)^2 + 2(1|(1cos(2π((2x - 2)/(1x - 2)) + 2))| - 1) + 3 and g(x) = (1(5(2|x - 3| + 3)^2 + 5(2|x - 3| + 3) - 1))/(-2(5(2|x - 3| + 3)^2 + 5(2|x - 3| + 3) - 1) - 2) between the vertical lines x ... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-2e^(2(-2|((3x + 1)/(-2x + 3)) - 2| + 1))) + 3| and g(x) = (3(2(1e^(-2x) + 1) + 5) - 1)/(2(2(1e^(-2x) + 1) + 5) - 3) from x = 0.6 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(1π((-2(1(-2|x - 2| - 3) + 2) + 1)/(-2(1(-2|x - 2| - 3) + 2) + 3)) - 2) + 1 and g(x) = (-2(5(1|x - 1| + 3)) - 1)/(-2(5(1|x - 1| + 3)) + 3) from x = 1.8 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3((-2(-1x^2) + 1)/(3(-1x^2) - 2))^2 - 5((-2(-1x^2) + 1)/(3(-1x^2) - 2)) - 1) - 1| + 1 and g(x) = 3|(1(-2|x + 1| - 2) + 4) + 2| between the vertical lines x = 0.8 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in La... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(2(-1(-1|x - 2| + 3)^2 - 3(-1|x - 2| + 3) + 3) - 3) + 5, g(x) = -2e^(-1(-5(3|x - 2| - 3) + 1)) - 3, x = 0.8, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 145.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2e^(1((3(1|x - 1| - 1) - 1)/(-1(1|x - 1| - 1) + 3)))) + 2| + 2 and g(x) = (1(-3cos(2π(5x^2 + 5x - 5))))/(-3(-3cos(2π(5x^2 + 5x - 5))) + 2) between the vertical lines x = -4.9 and x = -4.800000000000001. Round to 1 decimal place.... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(2π(-3|(-3|(2|x + 3| - 3) + 1| + 1) - 1| + 1) + 3) and g(x) = 2|((-2(3cos(1πx + 2) + 1) + 1)/(1(3cos(1πx + 2) + 1) - 2))| - 2 from x = -3.1 to x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 35.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5((-1(5(-4x - 2) + 5) - 2)/(2(5(-4x - 2) + 5) + 1)) + 4 and g(x) = 3(-1(-3|x + 3| - 3)^2 - 2(-3|x + 3| - 3) + 3)^2 + 3(-1(-3|x + 3| - 3)^2 - 2(-3|x + 3| - 3) + 3) + 4 from x = -3.1 to x = -2.9. Round to 1 decimal place.\n\nPresent the answe... | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-4(1((-1x - 3)/(-2x - 1)) - 4)^2 - 3(1((-1x - 3)/(-2x - 1)) - 4))^2 + 2 and g(x) = -4(2|(-2e^(1x) + 2)| - 1) - 1 between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-4(-1(4x + 2) - 5) + 5)^2 - 5(-4(-1(4x + 2) - 5) + 5) - 4 and g(x) = -1(2cos(2π(-1|x - 2| - 2) - 2) + 3)^2 - 4(2cos(2π(-1|x - 2| - 2) - 2) + 3) + 5 from x = -2.1 to x = -2.0. 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) = -5(2cos(1π(-2((2x - 1)/(2x + 2)) + 1) + 2) - 3) - 2, g(x) = 2(3(4x - 2) + 5)^2 - 5(3(4x - 2) + 5) - 5, x = -0.1, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-4((-3(-2x + 1) + 2)/(3(-2x + 1) - 2))^2) - 3 and g(x) = 5(-5(-4x^2 + 3x + 4) + 4) - 3 from x = -0.6 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 129.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1|(-4(3e^(-1x) - 3)^2 - 3(3e^(-1x) - 3) - 4) - 2|) and g(x) = (-1(1sin(3π(-2x + 3) + 2) + 1) + 3)/(2(1sin(3π(-2x + 3) + 2) + 1) - 3) between the vertical lines x = 4.5 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer i... | 3.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-2(-3|((2x)/(-1x + 2)) - 3| + 3) + 2)^2 - 4(-2(-3|((2x)/(-1x + 2)) - 3| + 3) + 2) - 2 and g(x) = 3|(-3((1x - 3)/(-1x - 1)) + 1) - 3| + 1 from x = 1.2 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-3e^(1(5(1x^2 + 4x + 5)^2 + 5(1x^2 + 4x + 5) + 5)) + 2) - 2)/(-3(-3e^(1(5(1x^2 + 4x + 5)^2 + 5(1x^2 + 4x + 5) + 5)) + 2) - 2), g(x) = 2cos(1π((-1(1|x - 1| - 3) + 2)/(2(1|x - 1| - 3) + 2)) - 3) - 3, x = 3.0, and x = 3.1. Round your answer ... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(3(-4(4x + 5) - 2)^2 - 5(-4(4x + 5) - 2) - 5)^2 - 2(3(-4(4x + 5) - 2)^2 - 5(-4(4x + 5) - 2) - 5) - 5, g(x) = 1(3(-3x^2 - 3x - 5) + 5) - 2, x = -1.5, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format:... | 23.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(2π(2|(1|(-5x - 3)| + 3)|) + 2) and g(x) = 1cos(1π((-2(-1|x + 1|) - 3)/(1(-1|x + 1|) + 1)) + 2) - 1 from x = 1.4 to x = 1.5. 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(-1e^(1(1((-3x - 1)/(2x + 2))^2 + 4((-3x - 1)/(2x + 2)) - 4)) - 2) + 2)/(2(-1e^(1(1((-3x - 1)/(2x + 2))^2 + 4((-3x - 1)/(2x + 2)) - 4)) - 2) + 2) and g(x) = -1(-2|((-2x + 2)/(1x + 3))| - 1)^2 - 3(-2|((-2x + 2)/(1x + 3))| - 1) - 3... | 8.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2((-1(2|(3|x - 1| - 2) - 1| - 3) - 1)/(2(2|(3|x - 1| - 2) - 1| - 3) - 3)) - 1)/(-1((-1(2|(3|x - 1| - 2) - 1| - 3) - 1)/(2(2|(3|x - 1| - 2) - 1| - 3) - 3)) - 2) and g(x) = -4(-4(-2e^(-1x) - 2)^2 - 1) - 5 from x = 0.9 to x = 1.1. Round to 1 ... | 25.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1((3(1|(2x^2 + 1x)| - 3))/(3(1|(2x^2 + 1x)| - 3) + 3)) + 2)/(3((3(1|(2x^2 + 1x)| - 3))/(3(1|(2x^2 + 1x)| - 3) + 3)) + 2) and g(x) = -3|(-1sin(1π(3|x - 3| - 3) - 1) - 1) + 3| - 1 from x = -1.4 to x = 0.9. Round to 1 decimal place.\n\nPresent... | 17.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3e^(-2(4((-2(-1|x - 1| + 1))/(2(-1|x - 1| + 1) - 1))^2 + 1((-2(-1|x - 1| + 1))/(2(-1|x - 1| + 1) - 1)) - 3)) - 1 and g(x) = -5((-3(2sin(2πx - 1) - 2) - 3)/(2(2sin(2πx - 1) - 2) - 1)) from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nP... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(4((1(3x + 4) + 3)/(1(3x + 4) + 2))^2 - 3((1(3x + 4) + 3)/(1(3x + 4) + 2)) - 4) - 3 and g(x) = 3sin(3π(5(-3|x| - 3)^2 + 1(-3|x| - 3) - 2) - 2) + 3 from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-1(5(-2|x + 1| - 1)^2 - 1) + 5) + 2)/(-1(-1(5(-2|x + 1| - 1)^2 - 1) + 5) - 2) and g(x) = -2e^(-2((3(3|x - 3| + 3) + 1)/(1(3|x - 3| + 3) + 2))) + 2 from x = -1.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2|(-3e^(-1(5x^2 + 5)) - 1) - 2| + 3) + 1 and g(x) = -5(2(4x - 1)^2 - 4(4x - 1) + 2)^2 + 5(2(4x - 1)^2 - 4(4x - 1) + 2) + 4 between the vertical lines x = 0.5 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex ... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3|(-1cos(2π(5x^2 + 1x + 3) - 3) + 3) + 2| - 2) - 1)/(2(3|(-1cos(2π(5x^2 + 1x + 3) - 3) + 3) + 2| - 2) - 1) and g(x) = (-3(-3((3x - 3)/(1x + 2))^2 + 5) - 3)/(1(-3((3x - 3)/(1x + 2))^2 + 5) - 2) between the vertical lines x = -0.0... | 53.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(1π(-5(2|(5x + 1)|) - 5) + 2) - 1, g(x) = -2(-3cos(3π(-5x + 5) + 2) - 2), x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-2cos(2π(1|((3x - 3)/(-1x - 1))| + 2)) - 1) - 3, g(x) = (-2(-5((-2x + 2)/(-2x - 2))^2 + 4((-2x + 2)/(-2x - 2)) + 3) - 3)/(-1(-5((-2x + 2)/(-2x - 2))^2 + 4((-2x + 2)/(-2x - 2)) + 3) + 2), x = -0.7, and x = -0.6. Round your answer to 1 deci... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(1(1cos(3π(2|x - 1| - 1) + 2) - 2)^2 - 4(1cos(3π(2|x - 1| - 1) + 2) - 2) + 3) + 1)/(-3(1(1cos(3π(2|x - 1| - 1) + 2) - 2)^2 - 4(1cos(3π(2|x - 1| - 1) + 2) - 2) + 3) - 1), g(x) = 2|(-1sin(3π(1|x + 2| + 3) - 2) - 1)| - 1, x = -3.1, and x = -3... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(5((-3(-3|x - 3| + 3) - 3)/(3(-3|x - 3| + 3) - 2))^2 + 5((-3(-3|x - 3| + 3) - 3)/(3(-3|x - 3| + 3) - 2)) - 3) - 1)/(1(5((-3(-3|x - 3| + 3) - 3)/(3(-3|x - 3| + 3) - 2))^2 + 5((-3(-3|x - 3| + 3) - 3)/(3(-3|x - 3| + 3) - 2)) - 3) + 2), g(x) ... | 19.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(3(2e^(1((-1x)/(-1x + 2))) - 2) + 4) - 3)/(2(3(2e^(1((-1x)/(-1x + 2))) - 2) + 4) - 1) and g(x) = 3(1((-3x + 3)/(1x - 2)) - 5) - 2 from x = 0.9 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 25.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(5(-4(-3sin(2πx) - 1) + 2)^2 - 5(-4(-3sin(2πx) - 1) + 2) - 4) + 3| + 1 and g(x) = 3|((2(1sin(3πx - 2) + 2))/(-1(1sin(3πx - 2) + 2) - 1)) + 3| + 3 from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 6.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(-3|(-4(2x^2 - 2x) + 1) - 2| + 3) - 3) + 3 and g(x) = -3((-3(-2|x - 1| + 2) + 1)/(2(-2|x - 1| + 2) + 1)) + 4 between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in L... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(1(-2(1sin(2πx) + 1) - 1))^2 + 2(1(-2(1sin(2πx) + 1) - 1)) - 3 and g(x) = 4(-1(3cos(3πx + 1) + 3)^2 - 2(3cos(3πx + 1) + 3) - 2) - 1 from x = 2.4 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 47.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(3sin(3π(-5(2|x + 1| - 2)^2 - 1(2|x + 1| - 2) - 2) - 3) - 1)| - 3 and g(x) = 2|(-1(-2e^(2x) + 3)^2 + 5(-2e^(2x) + 3) - 5)| + 3 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(2sin(3π((-1(-2x^2 + 5x + 5) + 3)/(1(-2x^2 + 5x + 5) + 1)) - 2) + 3)^2 - 1(2sin(3π((-1(-2x^2 + 5x + 5) + 3)/(1(-2x^2 + 5x + 5) + 1)) - 2) + 3) + 2, g(x) = -1e^(2((-3(-2|x - 2| + 1))/(-3(-2|x - 2| + 1)))) - 1, x = -1.0, and x = -0.9. Round ... | 1.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-5(-2|(-3x - 5) + 1| + 1)^2 + 5(-2|(-3x - 5) + 1| + 1) + 4) - 1 and g(x) = -2|(3((-3x + 3)/(2x - 1)) - 2) - 1| - 3 from x = -1.6 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 20.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(2|(2sin(3π(3x + 2) - 3) - 1) + 3| - 1)^2 - 2(2|(2sin(3π(3x + 2) - 3) - 1) + 3| - 1) + 4 and g(x) = 4((2(-3x + 5) - 2)/(-3(-3x + 5) - 1)) - 4 from x = -2.2 to x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 1.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(3π(-3|(-1|(3x - 2) - 2| + 2) - 2| - 3) + 2) - 3 and g(x) = 2(-1|(-5x + 3) - 1| + 1)^2 + 5(-1|(-5x + 3) - 1| + 1) - 3 from x = 0.7 to x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|((2((1x + 2)/(-3x)))/(-1((1x + 2)/(-3x)) + 2)) - 2| + 3)^2 - 5(-2|((2((1x + 2)/(-3x)))/(-1((1x + 2)/(-3x)) + 2)) - 2| + 3) - 2 and g(x) = (-2(-3sin(3π(-3x^2 + 5x + 3) - 2) - 3) - 1)/(-2(-3sin(3π(-3x^2 + 5x + 3) - 2) - 3) + 1) b... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((-2((2(5x - 4) - 2)/(-1(5x - 4) - 3)) + 1)/(1((2(5x - 4) - 2)/(-1(5x - 4) - 3)) + 3))^2 + 4((-2((2(5x - 4) - 2)/(-1(5x - 4) - 3)) + 1)/(1((2(5x - 4) - 2)/(-1(5x - 4) - 3)) + 3)) + 5 and g(x) = (-2(2sin(1π((3x - 3)/(3x - 2)) - 3) -... | 5.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(3(2|((-1x + 1)/(-3x + 2)) + 3| - 3)^2 - 1(2|((-1x + 1)/(-3x + 2)) + 3| - 3) + 3) + 1| - 1 and g(x) = 3((-2((2x + 1)/(-3x - 1)))/(1((2x + 1)/(-3x - 1)) - 3))^2 - 4((-2((2x + 1)/(-3x - 1)))/(1((2x + 1)/(-3x - 1)) - 3)) + 3 from x = 0.7 to x... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(3e^(-1(3(2x^2 + 3x - 5)^2 + 1))) - 2| + 1 and g(x) = -3|(-2(-5x + 5)^2 + 1(-5x + 5) + 4) + 1| - 1 from x = 1.2 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-3(2(4x - 1) + 5)^2 - 3(2(4x - 1) + 5) + 5)^2 + 5(-3(2(4x - 1) + 5)^2 - 3(2(4x - 1) + 5) + 5) + 4 and g(x) = -1((-1(-2|x + 1| - 2) - 1)/(2(-2|x + 1| - 2) - 1)) + 4 from x = -0.3 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer ... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-2(-3|(-1|x + 2| + 3) + 2| + 2) + 5) - 4 and g(x) = 3(-2sin(1π(-4x - 4) + 3)) - 4 from x = 2.5 to x = 2.7. 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|(-3(2sin(1π(-2x^2 - 1x + 2) - 2) + 1)^2 - 5(2sin(1π(-2x^2 - 1x + 2) - 2) + 1) - 5) + 1| + 3 and g(x) = 1|((1(3x - 1))/(-2(3x - 1) + 3)) + 2| + 1 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent ... | 11.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-2(1(-2x^2 + 1x + 3) + 1) - 3) + 2)/(2(-2(1(-2x^2 + 1x + 3) + 1) - 3)) and g(x) = 4(-2|(-3|x| + 2) - 1| + 3) + 5 from x = -1.0 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 18.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-1|(1|(3x + 4) + 1| + 1) - 3| - 1) + 5 and g(x) = 1|(4(4x - 2)^2 + 3(4x - 2) - 2) + 1| from x = 0.2 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-1(3|((-3(1|x + 2| - 1) - 1)/(-2(1|x + 2| - 1) - 2)) + 1| - 3)) - 3 and g(x) = -1(1cos(1π(-2|x + 1| - 1) - 2) - 1)^2 - 4(1cos(1π(-2|x + 1| - 1) - 2) - 1) + 4 between the vertical lines x = -2.3 and x = -1.7. Round to 1 decimal p... | 5.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1e^(1((-1(-2|(3|x| - 2) - 1| + 2) - 3)/(2(-2|(3|x| - 2) - 1| + 2) + 3))) - 3, g(x) = 5(4(-2cos(1πx + 2) + 2) - 5) + 5, x = -0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 29.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(2|(3(2|x - 1| - 2) + 4) - 1| - 2)^2 - 4(2|(3(2|x - 1| - 2) + 4) - 1| - 2) - 1 and g(x) = -1(1(-3|x - 2|))^2 between the vertical lines x = 1.3 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 1.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-2(2|(1sin(3πx - 2) + 2) - 2| - 3) - 1)/(-2(2|(1sin(3πx - 2) + 2) - 2| - 3) - 3)) + 2| + 3 and g(x) = -1((1(2|x + 3| - 3) + 2)/(3(2|x + 3| - 3) + 2)) - 5 between the vertical lines x = -1.9 and x = -1.7. Round to 1 decimal plac... | 7.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-4((-1(-2x - 3))/(2(-2x - 3) - 1)) + 1)^2 + 5(-4((-1(-2x - 3))/(2(-2x - 3) - 1)) + 1) + 4, g(x) = -2cos(3π(-1|(1|x - 1| - 1) + 2| + 2) + 1) + 2, x = -1.6, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex f... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(3(-1|(5x^2 + 4x - 3) + 3| + 1) - 4), g(x) = 2e^(-1(2(1x^2 + 1x - 1) + 5)) + 3, x = -0.8, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1e^(-1(1|(-5x + 5) - 3| + 1)) - 3))/(-2(-1e^(-1(1|(-5x + 5) - 3| + 1)) - 3) - 2) and g(x) = 1(-5(2x^2 + 4x)^2 - 4(2x^2 + 4x) - 1)^2 + 1(-5(2x^2 + 4x)^2 - 4(2x^2 + 4x) - 1) - 4 between the vertical lines x = -1.6 and x = -0.4. R... | 102.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1cos(1π(-1|(-1x^2 + 3) - 2| - 2) - 3) + 1) + 2)/(1(1cos(1π(-1|(-1x^2 + 3) - 2| - 2) - 3) + 1) - 3) and g(x) = 4(-1|(1x^2 + 4x) - 1| + 1)^2 - 3 between the vertical lines x = -4.2 and x = -4.0. Round to 1 decimal place.\n\nPresent... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|((-2((-1(-5x^2 - 4x + 5) - 1)/(-2(-5x^2 - 4x + 5) + 3)) - 2)/(-1((-1(-5x^2 - 4x + 5) - 1)/(-2(-5x^2 - 4x + 5) + 3)) + 3)) - 2| and g(x) = 1((3(-1|x - 2|) + 1)/(-1(-1|x - 2|))) - 5 from x = 1.8 to x = 2.2. Round to 1 decimal place.\n\nPres... | 42.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(1(-5(-1x^2 - 3x - 1))^2 + 5(-5(-1x^2 - 3x - 1)) + 3) + 4, g(x) = 1(2|(-1x) + 3| - 1) - 4, x = -2.1, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1π(2|(-1(3x^2 - 4x - 5) - 5) - 3| + 1) - 1) and g(x) = -2(2|(-3sin(3πx + 3) - 1) + 2| - 1)^2 - 2(2|(-3sin(3πx + 3) - 1) + 2| - 1) - 1 between the vertical lines x = -3.6 and x = -3.5. Round to 1 decimal place.\n\nPresent the an... | 1.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3|(-1(-1x^2 - 3x - 3) - 4) - 1| + 1) - 3)/(-2(-3|(-1(-1x^2 - 3x - 3) - 4) - 1| + 1) + 1) and g(x) = -2|(-1((-1x - 2)/(2x + 3)) + 4) + 2| - 3 between the vertical lines x = -3.5 and x = 0.5. Round to 1 decimal place.\n\nPresent t... | 76.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-5(-5(-5x^2 + 2x + 5)^2 - 4(-5x^2 + 2x + 5) + 1) - 4) - 2)/(2(-5(-5(-5x^2 + 2x + 5)^2 - 4(-5x^2 + 2x + 5) + 1) - 4) + 1) and g(x) = (2(-2|(-1|x + 1| + 3) - 2| + 3) + 3)/(1(-2|(-1|x + 1| + 3) - 2| + 3) - 3) between the vertical li... | 122.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(3π(2|((1(1|x| + 1))/(-2(1|x| + 1) - 2)) + 1| - 1) - 1), g(x) = -5((3(4x^2 + 3x + 1) - 2)/(3(4x^2 + 3x + 1) - 1))^2 + 3, x = -0.8, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2π(2((-2((2x)/(-2x - 3)) + 2)/(3((2x)/(-2x - 3)))) + 4) + 1) and g(x) = 4(1(-2x - 3)^2 + 4(-2x - 3) - 5) + 2 between the vertical lines x = -2.0 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 66.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1e^(-2(3|(2|(4x^2 + 5x - 4) + 3| - 3) - 1| - 2)) + 2, g(x) = -3((-1(2cos(1πx + 2)) + 3)/(1(2cos(1πx + 2)))) - 4, x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(5(1(-3sin(3πx + 1) - 1)^2 + 1(-3sin(3πx + 1) - 1) - 5) + 5) + 1| + 1 and g(x) = -3|((2(3|x - 3| - 1) - 2)/(-2(3|x - 3| - 1) + 1))| + 2 from x = -1.8 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 5.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3((1(-1|(3sin(3πx + 2)) + 3| + 2) + 1)/(-2(-1|(3sin(3πx + 2)) + 3| + 2) - 1)) + 3)/(-2((1(-1|(3sin(3πx + 2)) + 3| + 2) + 1)/(-2(-1|(3sin(3πx + 2)) + 3| + 2) - 1)) + 3) and g(x) = 1e^(-1(1((-3x - 3)/(-1x - 2))^2 - 3((-3x - 3)/(-1x -... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2|((-3(-1e^(-1x) + 3) - 1)/(-2(-1e^(-1x) + 3) - 3)) - 2|) + 1 and g(x) = 1(1|(-3sin(2πx - 2) - 2)| - 2)^2 - 3 between the vertical lines x = 3.5 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(1((3(3sin(1πx + 1)))/(-1(3sin(1πx + 1)) - 3))^2 - 2((3(3sin(1πx + 1)))/(-1(3sin(1πx + 1)) - 3)) - 2) + 4 and g(x) = -3e^(1(2(1x^2 - 5x - 5) + 3)) + 1 from x = 1.6 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 4.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1cos(2π(-2(3x^2 - 5x + 1) - 3) - 2) + 2) - 3)/(1(-1cos(2π(-2(3x^2 - 5x + 1) - 3) - 2) + 2) - 2) and g(x) = -3(3|(2|x - 3| - 2) - 2|) between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answe... | 4.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(1cos(1π(-2|((1x + 2)/(3x - 2)) + 1| - 2) + 2)) - 2, g(x) = (-1(-5(1cos(3πx) - 1) - 4) - 1)/(2(-5(1cos(3πx) - 1) - 4) + 1), x = 1.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(3(5(3x + 2)^2 + 5(3x + 2) - 4) + 1))/(-1(3(5(3x + 2)^2 + 5(3x + 2) - 4) + 1) + 2) and g(x) = (-3(1(-2e^(1x) - 1)) - 1)/(-1(1(-2e^(1x) - 1)) - 1) from x = -1.2 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 3.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((2(3|(3sin(2πx - 1) - 2) - 2|))/(-2(3|(3sin(2πx - 1) - 2) - 2|) + 3)) + 4 and g(x) = 3sin(2π(-4(2x^2 + 3x) + 4) - 3) - 3 between the vertical lines x = 3.0 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex form... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-1((-2(4x - 3) - 2)/(3(4x - 3))) + 3) + 3)/(3(-1((-2(4x - 3) - 2)/(3(4x - 3))) + 3) - 1) and g(x) = -1|(-5(-2|x + 3| + 3) - 3) + 1| + 2 from x = -1.5 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Y... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2((3(-2e^(-2(2x + 5)) - 3) - 1)/(-2(-2e^(-2(2x + 5)) - 3) + 1)) - 1)/(1((3(-2e^(-2(2x + 5)) - 3) - 1)/(-2(-2e^(-2(2x + 5)) - 3) + 1))), g(x) = 3|((1(-4x) + 2)/(1(-4x) - 3)) + 1| - 2, x = -0.4, and x = 2.1. Round your answer to 1 decimal pla... | 3.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-2|(-2|(-5x^2 - 4x - 2) - 3| + 2) - 2| - 2) + 2| - 2 and g(x) = (-3(3sin(2π(-4x^2 - 5x + 2) - 3) - 2) - 3)/(3(3sin(2π(-4x^2 - 5x + 2) - 3) - 2) + 2) between the vertical lines x = -0.2 and x = 0.0. Round to 1 decimal place.\n\nP... | 4.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1π(4(-5(-4x^2 - 1x + 5)^2 - 4(-4x^2 - 1x + 5) - 4) - 2) - 2) + 2 and g(x) = 3(-1|(-3x^2 - 1x + 4) + 1| - 2)^2 + 4(-1|(-3x^2 - 1x + 4) + 1| - 2) - 2 between the vertical lines x = 1.1 and x = 1.2000000000000002. Round to 1 decim... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(3π(-5(-3(2|x + 2| - 1) + 3)^2 - 4(-3(2|x + 2| - 1) + 3) - 2)) - 1 and g(x) = 1(2cos(1π(-3x) + 1) - 2)^2 - 4(2cos(1π(-3x) + 1) - 2) from x = -3.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 69.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-4(1sin(3π(1x + 2) + 2) - 3) - 3) + 1 and g(x) = 3e^(1((1(-1x^2 - 2) + 3)/(-2(-1x^2 - 2) - 2))) + 2 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"
}
] | 0.1 | MATH |
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