messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
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[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((-3((-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3) - 1)/(-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3))) + 2)/(3((-3(-1e^(-2((1((-3x)/(-2x - 1)) + 3)/(-1((-3x)/(-2x - 1)) + 2))) + 3) - 1)/(-3... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-3(-2|(1(3(2x^2 - 4x - 4)^2 - 1(2x^2 - 4x - 4) - 3) + 2) - 3| + 1) + 1) - 2, g(x) = 3(1e^(-1(1|(1|((1x + 1)/(3x - 2)) - 3| + 1) + 3| + 3)) + 2) - 3, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaT... | 2.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5((-1(2|(-5(3e^(-1(1|x - 1|)) - 1)^2 + 1(3e^(-1(1|x - 1|)) - 1) - 1)|) - 2)/(2(2|(-5(3e^(-1(1|x - 1|)) - 1)^2 + 1(3e^(-1(1|x - 1|)) - 1) - 1)|) - 1)) - 4 and g(x) = 1(-1|(-3(-3(-5x + 1)^2 - 3(-5x + 1) + 2) - 2) - 2|)^2 + 4(-1|(-3(-3(-5x + 1... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(-2((2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) - 1|) - 2)/(2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) - 1|) - 1)) + 4)^2 - 3(-2((2(-3|((-3((2x + 3)/(-1x + 2)) + 3)/(-3((2x + 3)/(-1x + 2)) + 1)) ... | 2.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(2π((-2((-3(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) + 2)/(-1(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) - 3)) - 3)/(1((-3(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) + 2)/(-1(4(3x^2 - 1x - 5)^2 - 5(3x^2 - 1x - 5) + 3) - 3)) - 3)))... | 50.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2(-4(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2))^2 - 2(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2)) + 2) + 4) + 1)/(-3(-2(-4(-3(-4(5x^2 - 5x - 2) + 2)^2 - 2(-4(5x^2 - 5x - 2) + 2))^2 - 2(-3(-4(5x^2 - 5x - ... | 40.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1((2(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2))/(-1(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2) - 1)) + 2)/(-1((2(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2))/(-1(1(-2|(5(1x - 3))|)^2 + 2(-2|(5(1x - 3))|) + 2) - 1)) + 2) and g(x... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(3π(-5(4(1((-3(2|x + 2| + 3) + 1)/(2(2|x + 2| + 3) + 3)) + 4)^2 - 3(1((-3(2|x + 2| + 3) + 1)/(2(2|x + 2| + 3) + 3)) + 4) + 2) + 2) - 1) - 1 and g(x) = 3cos(2π(-4(2|(-4(2|x| - 2)^2 + 5(2|x| - 2) - 2) + 1| - 1)^2 + 4) - 3) + 1 from x = 2.0... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-4(-3(3(1cos(2π((3x + 3)/(-2x)) - 3) - 1)^2 - 4(1cos(2π((3x + 3)/(-2x)) - 3) - 1) + 1)^2 + 4(3(1cos(2π((3x + 3)/(-2x)) - 3) - 1)^2 - 4(1cos(2π((3x + 3)/(-2x)) - 3) - 1) + 1)) + 3) + 2, g(x) = 4(-5(-2|(-5(-1x^2 - 3x) + 2) + 2| + 2)^2) + 2, ... | 313.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(-1|(3((2((1((3x + 3)/(2x - 1)) + 1)/(-3((3x + 3)/(2x - 1)) - 1)) - 3)/(2((1((3x + 3)/(2x - 1)) + 1)/(-3((3x + 3)/(2x - 1)) - 1)) - 1)) + 3) + 2| + 3) - 2| + 3 and g(x) = 3(2(-1cos(2π(1((-3x - 3)/(2x + 2)) - 4) + 3) - 2)^2 + 5(-1cos(2π(1((... | 46.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2cos(2π(-2|(-1(-1(-4(3x^2 - 3x - 2)^2) + 1) + 2) - 1|) + 2) - 2, g(x) = -3|((3(1sin(1π(-5(-2x - 2)^2 + 5(-2x - 2) + 5) - 3) + 2) + 2)/(-2(1sin(1π(-5(-2x - 2)^2 + 5(-2x - 2) + 5) - 3) + 2))) + 3| - 2, x = 0.6, and x = 0.7. Round your answer t... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(2|((-1(-2(2|(1|x| + 1) - 3|) + 4) + 2)/(-2(-2(2|(1|x| + 1) - 3|) + 4) - 2)) - 2|) - 2, g(x) = -3e^(-2(3|(1|(1|((2x - 1)/(-2x + 3)) - 3| - 2) - 2| - 3) + 2| - 3)) - 1, x = -3.4, and x = -2.6. Round your answer to 1 decimal place.\n\nPresen... | 103.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-2|(5((-2((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) - 2)/(-1((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) + 3))^2 + 4((-2((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) - 2)/(-1((-1(2|x + 2| - 3) + 3)/(-2(2|x + 2| - 3) - 1)) + 3)) ... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1((-3(-2((-1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)) + 1)/(1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)))) - 1))/(2(-2((-1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)) + 1)/(1((2(-2|x - 3| - 1) + 1)/(1(-2|x - 3| - 1) + 3)))) - 1... | 2.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((1(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3) - 1)/(-2(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3)))^2 + 2((1(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3) - 1)/(-2(2|(2|(1|((1x)/(-3x + 2)) + 2| + 2) + 3|) - 3| - 3))) +... | 2.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((3(-2((-2((-2(-1x - 1))/(2(-1x - 1) + 1)))/(-1((-2(-1x - 1))/(2(-1x - 1) + 1)) - 1)) + 4) - 2)/(-1(-2((-2((-2(-1x - 1))/(2(-1x - 1) + 1)))/(-1((-2(-1x - 1))/(2(-1x - 1) + 1)) - 1)) + 4) - 2)), g(x) = -3|((2(-3|(1(-5x^2 - 3x + 3) + 2) - 3| ... | 2.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-3(4((-2((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)/(-3((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)) - 4) - 4) - 2)/(2(-3(4((-2((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)/(-3((-2(5x^2 - 2))/(-2(5x^2 - 2) + 3)) - 3)) - 4) - 4) - 3), g(x) = -2|(-1|(... | 9.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-1|(-4(-1cos(2π(-1((-3x - 1)/(2x - 1))^2 + 1((-3x - 1)/(2x - 1)) - 3) + 3)) + 3) + 3|) + 2)/(-1(-1|(-4(-1cos(2π(-1((-3x - 1)/(2x - 1))^2 + 1((-3x - 1)/(2x - 1)) - 3) + 3)) + 3) + 3|)), g(x) = 1|(1(-3sin(1π(4(-3x^2 + 3x + 4)^2 - 4(-3x^2 +... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-1((-1(5(1(3(-3x + 5) - 2) - 5) + 3) + 1)/(3(5(1(3(-3x + 5) - 2) - 5) + 3) + 2))) and g(x) = (2(-4((1(-2|(-2sin(3πx - 1) - 1)| + 1) - 1)/(-2(-2|(-2sin(3πx - 1) - 1)| + 1) + 1))^2 + 1((1(-2|(-2sin(3πx - 1) - 1)| + 1) - 1)/(-2(-2|... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(1π(2|(-3|((2(-4((3x + 2)/(-1x + 2)) - 3) - 3)/(-2(-4((3x + 2)/(-1x + 2)) - 3) - 1)) - 1| - 2) - 3|) + 3) - 2 and g(x) = (1((-1(2sin(3π(-1((-2x + 2)/(3x - 2))^2 + 3((-2x + 2)/(3x - 2)) + 3) + 1) + 1))/(-2(2sin(3π(-1((-2x + 2)/(3x - 2))^... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(3(-1|(-2((3((-1x + 1)/(-2x + 3)) + 3)/(3((-1x + 1)/(-2x + 3)) - 2)) + 1)| + 3) + 2) - 3| + 1, g(x) = -3(-2e^(-2(2|(5(3x^2 + 2x + 1) + 4) - 2| + 3)) + 1)^2 + 3(-2e^(-2(2|(5(3x^2 + 2x + 1) + 4) - 2| + 3)) + 1) - 2, x = 1.1, and x = 1.2. Ro... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3e^(2(4(-1|(1|(1x^2 + 4x + 4)| + 1) - 3| - 3) + 5)) - 2) - 3)/(-3(3e^(2(4(-1|(1|(1x^2 + 4x + 4)| + 1) - 3| - 3) + 5)) - 2) - 1) and g(x) = (-2(1|(-1(-3sin(2π(1|x - 1| + 2) + 2) + 2)^2 + 5(-3sin(2π(1|x - 1| + 2) + 2) + 2) - 3)|) ... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(2cos(1π(2|(4((-2(-2x^2 - 2x) + 3)/(1(-2x^2 - 2x)))) + 3|) + 3) - 2) - 3)/(-3(2cos(1π(2|(4((-2(-2x^2 - 2x) + 3)/(1(-2x^2 - 2x)))) + 3|) + 3) - 2) - 3), g(x) = 1((-2((1(-2(1|x + 3| + 1) - 2) - 3)/(2(-2(1|x + 3| + 1) - 2) + 2)))/(-2((1(-2(1|... | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-3(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) - 2)/(-2(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) + 3)) + 3)/(-3((-3(3(3|(2(1x - 4) + 3)| + 3)^2 + 3(3|(2(1x - 4) + 3)| + 3) - 5) - 2)/(-2(3(3|... | 1.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((1(-3(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1)^2 + 1(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1) + 1) + 1)/(-3(-3(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1)^2 + 1(-2((3(-4x - 3) + 3)/(3(-4x - 3) + 3)) - 1) + 1)))^2 - 5((1(-3(-2((... | 3.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1) + 3) + 3))^2 + 3((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1) + 3) + 3)) - 1)^2 - 5(-1((-2(1(-2(1e^(-1x) - 1) - 1) + 3) - 2)/(1(1(-2(1e^(-1x) - 1) - 1)... | 3.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(-2(1sin(2π((-1((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) - 2)/(2((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) + 1))) - 3)^2 - 2(1sin(2π((-1((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) - 2)/(2((-2(-2|x - 3|) + 3)/(1(-2|x - 3|) + 2)) + 1))) - 3) + 2)... | 290.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-1(-3cos(1π((1(2((1x - 3)/(-2x)) + 5) - 2)/(-2(2((1x - 3)/(-2x)) + 5) - 3)) + 2) - 3) - 3)/(2(-3cos(1π((1(2((1x - 3)/(-2x)) + 5) - 2)/(-2(2((1x - 3)/(-2x)) + 5) - 3)) + 2) - 3) - 1)) + 1)/(-1((-1(-3cos(1π((1(2((1x - 3)/(-2x)) +... | 6.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(3(2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1)^2 - 2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1) + 1)^2 - 3(2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1)^2 - 2(2(-4(1x + 5) + 2)^2 - 5(-4(1x + 5) + 2) + 1) + 1) - 5) + 1, g(x) = (2((-1(... | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1(-1(2|(-2|(-2cos(2πx + 3) + 2)|) - 3|) + 5)^2 - 3(-1(2|(-2|(-2cos(2πx + 3) + 2)|) - 3|) + 5) - 5) + 1| + 3 and g(x) = 5(4(3cos(1π(-3(-3x^2 + 3x - 4) - 2) - 2) - 2) - 3) - 5 between the vertical lines x = 0.7 and x = 1.4. Round ... | 227.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((-3(4((2(-1|(-2|x + 3| - 1) + 2|) - 3)/(3(-1|(-2|x + 3| - 1) + 2|) + 1))))/(-3(4((2(-1|(-2|x + 3| - 1) + 2|) - 3)/(3(-1|(-2|x + 3| - 1) + 2|) + 1))) - 1)) - 2 and g(x) = -5(4(3((-2(2sin(1πx - 3) - 1))/(-1(2sin(1πx - 3) - 1) + 2))^2 - 2((-... | 40.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2e^(-2(1((-3(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 2)/(1(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 3))^2 + 2((-3(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 2)/(1(2|(-4((-2x - 2)/(1x - 3))) + 3|) - 3)) - 4)) and g(x) = 1cos(2π(-5((-1(1|(3x - 1) + 2| + 3) - 3)... | 3.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1|(-2|(-3((-2(-5x^2 - 4x - 1))/(3(-5x^2 - 4x - 1) + 2)) - 5)| - 3)| + 3) + 3)/(-2(1|(-2|(-3((-2(-5x^2 - 4x - 1))/(3(-5x^2 - 4x - 1) + 2)) - 5)| - 3)| + 3) - 3) and g(x) = 2cos(3π(-4(3|(5(5x + 5)^2 - 1(5x + 5) - 4) - 1| + 3)^2 - 2... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(1(-4((1((2(3x + 3) + 1)/(-1(3x + 3) + 2)) - 3)/(3((2(3x + 3) + 1)/(-1(3x + 3) + 2)) + 3)) + 3)^2 - 1(-4((1((2(3x + 3) + 1)/(-1(3x + 3) + 2)) - 3)/(3((2(3x + 3) + 1)/(-1(3x + 3) + 2)) + 3)) + 3) - 1) - 3, g(x) = 2((1(3|(-2sin(3π((1x)/(1x)) ... | 3.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(2|((-1(4(-4(2|x - 2| - 2) + 3) - 1) - 1)/(1(4(-4(2|x - 2| - 2) + 3) - 1) - 3)) + 3| - 3)^2 + 4(2|((-1(4(-4(2|x - 2| - 2) + 3) - 1) - 1)/(1(4(-4(2|x - 2| - 2) + 3) - 1) - 3)) + 3| - 3) + 5, g(x) = -5((1(2|((-1(-3x - 5))/(1(-3x - 5) + 3)) -... | 1.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(1π((-3(-1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3))^2 + 1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3)) - 5) - 3)/(-2(-1((-1(5((3x + 3)/(2x)) + 2))/(-2(5((3x + 3)/(2x)) + 2) + 3))^2 + 1((-1(5((3x + 3)/(2x))... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4(-1(5(-1e^(1(-3|x - 2|)) - 1) + 2) - 2) - 4) - 2)/(-2(-4(-1(5(-1e^(1(-3|x - 2|)) - 1) + 2) - 2) - 4) + 3) and g(x) = (-1(2|(-1|((3(2|x - 3|) - 2)/(-2(2|x - 3|) + 3)) - 2| + 2) - 2| - 2) - 3)/(-2(2|(-1|((3(2|x - 3|) - 2)/(-2(2|... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((1(-3(3|((-2(1sin(1πx) - 2) + 3)/(-2(1sin(1πx) - 2) - 1)) - 3|)^2 + 3(3|((-2(1sin(1πx) - 2) + 3)/(-2(1sin(1πx) - 2) - 1)) - 3|) - 3) + 1)/(-1(-3(3|((-2(1sin(1πx) - 2) + 3)/(-2(1sin(1πx) - 2) - 1)) - 3|)^2 + 3(3|((-2(1sin(1πx) - 2) + 3)/(-... | 1.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(1|(2|((-2(1(1|x| - 3) + 2) + 1)/(1(1(1|x| - 3) + 2) - 2)) + 1| - 1) - 1| - 2)^2 - 1(1|(2|((-2(1(1|x| - 3) + 2) + 1)/(1(1(1|x| - 3) + 2) - 2)) + 1| - 1) - 1| - 2) - 3 and g(x) = 1(-1(2(1(-1|x - 1| - 3) - 5) + 2) - 5)^2 + 2 from x = 2.6 to x... | -2131.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(1π((2(5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3) - 1)/(2(4x + 3) + 2)))^2 - 5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3) - 1)/(2(4x + 3) + 2))) - 2) + 3)/(3(5(4((-3(4x + 3) - 1)/(2(4x + 3) + 2))^2 + 5((-3(4x + 3... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-3(1(-5((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3))^2 - 3((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3)) + 2) + 3)^2 - 4(1(-5((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3))^2 - 3((2(3|x + 2|) + 3)/(-2(3|x + 2|) + 3)) + 2) + 3) - 1) - 3)/(2(-3(1(-5((2(3|x + 2|) +... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((1(-5(2((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2))^2 - 3((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2)) - 5) - 3) - 2)/(1(-5(2((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) + 2) - 2))^2 - 3((-3(-1e^(-1x) + 2) + 1)/(-2(-1e^(-1x) +... | 2.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(1cos(3π((-1(2(1(3x) + 1) - 5) + 2)/(-1(2(1(3x) + 1) - 5) - 3)) + 3)) - 1)/(-3(1cos(3π((-1(2(1(3x) + 1) - 5) + 2)/(-1(2(1(3x) + 1) - 5) - 3)) + 3)) - 1) and g(x) = (-1((1(-2(-1|((2x)/(-2x + 3)) - 1| + 3) - 2))/(-1(-2(-1|((2x)/(-2x + 3)) -... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1(-4(-2(-1((3x - 2)/(-3x)) - 3)^2 + 4)^2 - 1(-2(-1((3x - 2)/(-3x)) - 3)^2 + 4) - 3) - 4) + 1| - 3 and g(x) = 3|(1(-5(1(1x^2 - 4x - 1) - 2)^2 + 2(1(1x^2 - 4x - 1) - 2) + 4)^2 - 2(-5(1(1x^2 - 4x - 1) - 2)^2 + 2(1(1x^2 - 4x - 1) - 2... | 27.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(3sin(3π(-2|((-2((-3(-2|x + 2| - 3) - 1)/(2(-2|x + 2| - 3) + 1)) + 1)/(-1((-3(-2|x + 2| - 3) - 1)/(2(-2|x + 2| - 3) + 1)) - 1)) + 2| - 1) - 1) + 2)| + 1, g(x) = 1(-3|(5(-2(-5x^2 - 4x + 2)^2 + 5(-5x^2 - 4x + 2) - 3) + 5) - 2| + 1), x = 0.0... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((2(-1sin(3π((2((-3(-5x - 2) - 2)/(1(-5x - 2))) - 2)/(1((-3(-5x - 2) - 2)/(1(-5x - 2))) + 3)) - 3) + 1) - 2)/(1(-1sin(3π((2((-3(-5x - 2) - 2)/(1(-5x - 2))) - 2)/(1((-3(-5x - 2) - 2)/(1(-5x - 2))) + 3)) - 3) + 1) + 2))^2 + 2((2(-1si... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((1(1(-5(2sin(1π(-1x^2 - 3x - 2) + 1) - 1) + 2)^2 - 4(-5(2sin(1π(-1x^2 - 3x - 2) + 1) - 1) + 2) - 5))/(-3(1(-5(2sin(1π(-1x^2 - 3x - 2) + 1) - 1) + 2)^2 - 4(-5(2sin(1π(-1x^2 - 3x - 2) + 1) - 1) + 2) - 5) + 1)) + 1, g(x) = (2(3((-2(2(-3|x + ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(4(1(-5(-4(-3x^2 - 4x + 4))^2 + 2)^2 - 1(-5(-4(-3x^2 - 4x + 4))^2 + 2) - 1) + 5))/(-3(4(1(-5(-4(-3x^2 - 4x + 4))^2 + 2)^2 - 1(-5(-4(-3x^2 - 4x + 4))^2 + 2) - 1) + 5) + 2), g(x) = (1(4(1(3|(1sin(2πx + 1) + 2)|) - 1) + 2))/(-1(4(1(3|(1sin(2π... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(1|(-1|(-5((3(3cos(3πx - 2) + 3) - 2)/(-3(3cos(3πx - 2) + 3) - 2)) - 5) + 1| + 1)| - 3) + 4 and g(x) = 1e^(2(1(2|(-4(-4x - 3) - 2) - 3|))) from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2cos(1π(-4(-3((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1))^2 + 4((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1)))^2 + 2(-3((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - 1))^2 + 4((1(-1x^2 + 4x + 4) - 1)/(2(-1x^2 + 4x + 4) - ... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(-3(-4(1((-3x + 1)/(-2x + 3))^2 - 3((-3x + 1)/(-2x + 3)) - 3) - 2) - 5)^2 - 4(-3(-4(1((-3x + 1)/(-2x + 3))^2 - 3((-3x + 1)/(-2x + 3)) - 3) - 2) - 5) - 5) - 3 and g(x) = (3(2|((2(1|(2x + 3) - 3| + 3) + 3)/(-3(1|(2x + 3) - 3| + 3... | 8.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1)^2 - 1(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1) - 4)^2 + 2(3(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1)^2 - 1(-2|(1|(4(5x + 4) - 1) + 3| + 1) - 3| + 1) - 4) - 2 and g(x) = (-1(-5(-1(3(2|x... | 10.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1e^(1(-2(2|(-2(-4((2x + 3)/(-3x - 3)) + 5)^2 + 1(-4((2x + 3)/(-3x - 3)) + 5)) + 3| - 3) - 1)) - 2, g(x) = (2((-1(3|((-3(2cos(2πx - 2) - 1))/(-2(2cos(2πx - 2) - 1) + 3)) + 2| - 3) - 1)/(1(3|((-3(2cos(2πx - 2) - 1))/(-2(2cos(2πx - 2) - 1) + 3... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4))^2 + 5(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4)) + 2) - 1)/(-1(1(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4))^2 + 5(-4(-4(3(-1x + 2) - 5)^2 + 3(3(-1x + 2) - 5) + 4)... | 50.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2(4(1(1|((2x - 3)/(-3x - 3)) - 1| + 1) - 2)^2 - 5(1(1|((2x - 3)/(-3x - 3)) - 1| + 1) - 2) + 3) + 5) + 1| - 2 and g(x) = 3e^(2(-1|(1|((-1(-1x^2 - 3x + 5))/(-1(-1x^2 - 3x + 5) + 2)) - 3| + 1) - 1| + 3)) + 2 between the vertical li... | 217.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((2((2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)/(-2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)) - 1)/(1((2(3(-2|(2|x| - 2) + 1| + 2)^2 + 2(-2|(2|x| - 2) + 1| + 2) - 2) - 2)/(-2(3(-2|... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1(2(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3)^2 - 1(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3))^2 - 2(2(-1(1|(1|x + 2| - 2) - 1| + 3)^2 + 4(1|(1|x + 2| - 2) - 1| + 3) + 3)^2 - 1... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((-2(-4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1)^2 + 4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1) - 2) - 1)/(-1(-4(4((-3((3x - 1)/(-3x - 3)) + 2)/(2((3x - 1)/(-3x - 3)))) - 1)^2 + 4(4((-3((3x - 1)/(-3... | 138.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-5(3(-1(2sin(1πx - 3) + 1) + 1) + 4) - 5)^2 + 2(-5(3(-1(2sin(1πx - 3) + 1) + 1) + 4) - 5) + 4) - 3)/(-3(1(-5(3(-1(2sin(1πx - 3) + 1) + 1) + 4) - 5)^2 + 2(-5(3(-1(2sin(1πx - 3) + 1) + 1) + 4) - 5) + 4) - 3), g(x) = -3(5(3|((-2(-5x + 2) ... | 4.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1|(1|(4((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1))^2 - 3((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1)) - 4) + 3| - 3)| + 1) - 3, g(x) = -1(1|((-2(-5(1cos(2πx - 1)) + 3) - 3)/(-2(-5(1cos(2πx - 1)) + 3) + 1))| - 1) + 1, x = -2.1, and x... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1e^(1(-4(1((-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)))/(-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)) + 1)) + 3)^2 + 3(1((-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)))/(-3((2(5x^2 + 2x - 2) + 2)/(2(5x^2 + 2x - 2) + 1)) + 1))... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1(3((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2)))^2 - 4((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2))) + 2))^2 + 2(-1(3((-1(3e^(-1(1|x| + 1)) - 2) - 3)/(1(3e^(-1(1|x| + 1)) - 2)))^2 - 4((-1(3e^(-1(1|x|... | 5.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-5(-1e^(1(-2|(-5(-4x - 5)^2 + 2(-4x - 5) + 4) + 2| - 3))) - 5) - 2)/(1(-5(-1e^(1(-2|(-5(-4x - 5)^2 + 2(-4x - 5) + 4) + 2| - 3))) - 5) - 2) and g(x) = -1cos(3π(-5(-4((2(-2|x + 2| + 1) + 2)/(-2(-2|x + 2| + 1) - 1)) - 3) + 5) + 2) - 1 from ... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3|((1(2|((-3(-1x^2 - 2x - 1) - 1)/(2(-1x^2 - 2x - 1))) - 3|) - 2)/(-3(2|((-3(-1x^2 - 2x - 1) - 1)/(2(-1x^2 - 2x - 1))) - 3|) - 2)) + 1| + 3) + 1 and g(x) = (-3(-1|(2|(-5(-1x^2 + 4x - 3)^2 + 1(-1x^2 + 4x - 3) + 5) + 1| + 3) - 2| +... | 9.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1(2|(-1(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)^2 - 2(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)) - 1| + 3) + 3)^2 - 3(-1(2|(-1(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)^2 - 2(5(2x^2 - 2x - 5)^2 + 1(2x^2 - 2x - 5) - 2)) - 1| ... | 0.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((1(-1cos(2π(-5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3)^2 + 5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3) + 3)) + 3) - 3)/(-3(-1cos(2π(-5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3)^2 + 5(-3(3x^2 - 4x - 5)^2 - 1(3x^2 - 4x - 5) + 3) + 3)... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-5(-3((3((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) - 1)/(2((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) + 2))^2 - 4((3((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)) - 1)/(2((2(-4x^2 + 1x + 4) - 3)/(-2(-4x^2 + 1x + 4) + 1)... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2e^(-1((-1(-3(-2|(2(-1x^2 + 3x) + 5)| - 3)^2 + 4(-2|(2(-1x^2 + 3x) + 5)| - 3) - 3) - 1)/(3(-3(-2|(2(-1x^2 + 3x) + 5)| - 3)^2 + 4(-2|(2(-1x^2 + 3x) + 5)| - 3) - 3) + 3))) and g(x) = (-1(2(2e^(-1(2((2x - 1)/(-2x - 3))^2 + 5((2x - 1)/(-2x - 3))... | 15.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1((1(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 1)/(2(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 2))^2 - 1((1(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 1)/(2(-5(1((-1x - 2)/(2x + 2)) + 2) + 2) + 2)) - 3) - 1| + 2 and g(x) = -2|(5(-3sin(3π(2|((-1x + 3)/(-... | 2.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2) + 3)/(1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2)))^2 + 4((1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2) + 3)/(1(-1|(-5(3|((1x - 3)/(2x)) + 1| - 1) - 3) - 1| + 2))) - 2 an... | -7.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2e^(1((-3(3|(-3(-1|(5x - 3)| + 1)^2 - 1) + 2| - 2) + 1)/(1(3|(-3(-1|(5x - 3)| + 1)^2 - 1) + 2| - 2) - 2))) + 2, g(x) = -4(1e^(1((3((1((-2x)/(2x + 3)) - 2)/(-2((-2x)/(2x + 3)) - 2)) - 2)/(1((1((-2x)/(2x + 3)) - 2)/(-2((-2x)/(2x + 3)) - 2)) + ... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(1|(-2sin(1π(-3|((-1(1|x + 2|) - 1)/(3(1|x + 2|) - 1)) - 3|) - 1) - 1) - 3| - 2) + 3)/(1(1|(-2sin(1π(-3|((-1(1|x + 2|) - 1)/(3(1|x + 2|) - 1)) - 3|) - 1) - 1) - 3| - 2)), g(x) = 1|(2((1(-3(2sin(1πx) + 3)^2 + 1(2sin(1πx) + 3) + 3) - 3)/(-1(... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1(5(2(-1(5x^2 + 1) + 1) - 3)^2 + 1(2(-1(5x^2 + 1) + 1) - 3) - 2) + 3) - 3| - 3 and g(x) = 3(-4((2((1(3x + 4) - 3)/(-3(3x + 4) - 2)) + 2)/(-2((1(3x + 4) - 3)/(-3(3x + 4) - 2)) + 1)) - 5)^2 - 1(-4((2((1(3x + 4) - 3)/(-3(3x + 4) - 2... | -770.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1((2(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1)^2 - 3(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1) + 3) + 1)/(3(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1)^2 - 3(-2((3(1x + 2) - 2)/(1(1x + 2))) - 1) + 3) + 3)) + 3)/(2((2(5(-2((3(1x + 2) - 2)/(1(1x + 2))) - ... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(-3|((-3(-3e^(1((2x + 2)/(1x - 3))) + 1))/(1(-3e^(1((2x + 2)/(1x - 3))) + 1) + 2)) - 2| + 1) - 2)/(3(-3|((-3(-3e^(1((2x + 2)/(1x - 3))) + 1))/(1(-3e^(1((2x + 2)/(1x - 3))) + 1) + 2)) - 2| + 1)))^2 + 1((-2(-3|((-3(-3e^(1((2x + 2... | 342.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-2((2(-1|(-1|((-1x - 2)/(1x + 2)) + 3|) - 2|) + 1)/(-2(-1|(-1|((-1x - 2)/(1x + 2)) + 3|) - 2|) + 3)) - 2) - 3, g(x) = -5(4((3(-3|(3sin(1πx + 1) + 1) - 3| + 3))/(-2(-3|(3sin(1πx + 1) + 1) - 3| + 3) + 1))^2 + 3((3(-3|(3sin(1πx + 1) + 1) - 3|... | 23.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(2e^(-1(-2((-1((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)) + 3)/(-3((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)))) - 5))) - 3)/(-1(2e^(-1(-2((-1((-2((-1x)/(3x + 1)) - 2)/(2((-1x)/(3x + 1)) - 3)) + 3)/(-3((-2((-1x)/(3x +... | 186.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-1(-1|(1(3(5x^2 + 3x - 4) + 4)^2 + 5) - 1| - 2) + 3)/(3(-1|(1(3(5x^2 + 3x - 4) + 4)^2 + 5) - 1| - 2) - 1)) + 1 and g(x) = 3((-2(2sin(1π(-3|(2x^2 + 4x + 2) + 1| + 2) - 2) + 3) + 3)/(-1(2sin(1π(-3|(2x^2 + 4x + 2) + 1| + 2) - 2) + 3) - 1)) +... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-5(-1(-4((2(-5x^2 - 3x - 2) + 2)/(2(-5x^2 - 3x - 2) + 3)) + 3) - 2) + 5) + 1)/(-2(-5(-1(-4((2(-5x^2 - 3x - 2) + 2)/(2(-5x^2 - 3x - 2) + 3)) + 3) - 2) + 5) - 2), g(x) = (1(-3(2(2e^(2(-2x^2 - 2x - 3)) + 2)^2 - 2(2e^(2(-2x^2 - 2x - 3)) + 2)... | 2.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3((2(-2(2(-1(1cos(3πx + 2) - 2) - 3) + 2) + 4) - 2)/(-2(-2(2(-1(1cos(3πx + 2) - 2) - 3) + 2) + 4) + 3)) and g(x) = -1(-2|((-1(-1sin(3π(-5x^2 + 4x - 4) - 3) - 3) - 2)/(3(-1sin(3π(-5x^2 + 4x - 4) - 3) - 3) + 3)) - 1| - 1) - 3 from x = -2.6 to ... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2(1(1(1(3|x - 2|) - 4)^2 - 3) - 5)) + 4 and g(x) = -1|((-1(-2sin(1π(-2|(-5x^2 + 1x - 1) + 2| + 2) + 3) + 3) - 2)/(2(-2sin(1π(-2|(-5x^2 + 1x - 1) + 2| + 2) + 3) + 3))) + 2| - 3 between the vertical lines x = 4.0 and x = 4.1. Round ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((-1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4) + 1)/(1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4)))^2 + 2((-1(1(1(-2(-5x^2 - 2x + 1)^2 + 3(-5x^2 - 2x + 1) + 5) - 1) - 4) + 1)/(1(1(1(-2(-5x^2 - 2x + 1)^2 + ... | 4.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3((-2(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) - 3)/(3(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) + 1)))/(-2((-2(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) - 3)/(3(5(3|(-1|(2|x| + 1) - 1| + 3)| - 2) + 3) + 1)) - 2) and g(x) = 2|((-1(-4(1((1x - 2)/... | 21.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-3(-1(2|(2(4x) + 5) + 2| + 1) + 5) - 1)/(1(-1(2|(2(4x) + 5) + 2| + 1) + 5) + 3))^2 + 3((-3(-1(2|(2(4x) + 5) + 2| + 1) + 5) - 1)/(1(-1(2|(2(4x) + 5) + 2| + 1) + 5) + 3)) - 5 and g(x) = (1(-3e^(-1(-5(3|(-1|x + 2| + 2) - 3| + 3) - 2)) - 1) -... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(1cos(3π((2(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) - 1)/(-3(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) + 1)) + 1) + 2)^2 - 2(1cos(3π((2(1|(1((2x)/(1x + 1))^2 + 2((2x)/(1x + 1))) + 1| - 3) - 1)/(-3(1|(1((2x)/(1x + 1))^... | 30.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(-1|(3(2|((1x)/(1x + 1)) - 2| - 2)^2 - 1(2|((1x)/(1x + 1)) - 2| - 2) - 1) + 3| - 1) - 1| + 1)^2 - 4(-1|(-1|(3(2|((1x)/(1x + 1)) - 2| - 2)^2 - 1(2|((1x)/(1x + 1)) - 2| - 2) - 1) + 3| - 1) - 1| + 1) - 4 and g(x) = -3|(1(-1((-2((... | -24.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4((2(-3(-5(-1(1x - 2) - 3) - 3)^2 - 3(-5(-1(1x - 2) - 3) - 3) + 5) - 2)/(-1(-3(-5(-1(1x - 2) - 3) - 3)^2 - 3(-5(-1(1x - 2) - 3) - 3) + 5) + 2)) + 3 and g(x) = -1((-1(2|(1sin(3π(1x^2 + 2x) - 3) - 3) - 1| - 3) - 2)/(2(2|(1sin(3π(1x^2 + 2x) - 3... | 11.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(1|(1(2(-1((-1x - 3)/(1x))^2 - 2((-1x - 3)/(1x)) + 2)^2 + 5(-1((-1x - 3)/(1x))^2 - 2((-1x - 3)/(1x)) + 2) + 1) - 4) + 2| - 3), g(x) = 1sin(2π(1((-3(4(-1x - 2)^2 - 4(-1x - 2)) - 3)/(-1(4(-1x - 2)^2 - 4(-1x - 2)) - 2)) + 2) - 2) + 2, x = -2.0... | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|((2((-1(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|)) - 3) + 3)/(-2(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|)) - 3))) + 1)/(2((-1(1(5(1|x - 2|)^2 + 3(1|x - 2|))^2 - 1(5(1|x - 2|)^2 + 3(1|x - 2|))... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-3cos(2π(4((-1(-3|((-3x)/(2x - 3)) + 1| - 3) - 1)/(2(-3|((-3x)/(2x - 3)) + 1| - 3) + 1))^2 - 3((-1(-3|((-3x)/(2x - 3)) + 1| - 3) - 1)/(2(-3|((-3x)/(2x - 3)) + 1| - 3) + 1)) - 5)) - 2) + 3)/(2(-3cos(2π(4((-1(-3|((-3x)/(2x - 3)) + 1| - 3) ... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2(-1|(3|(5(-3x + 4)^2 - 3(-3x + 4) + 1) - 2| - 1) - 3|) - 2) - 4 and g(x) = (-2(5(3|(-1(1x + 4) + 3) - 2| - 3) - 4) + 2)/(2(5(3|(-1(1x + 4) + 3) - 2| - 3) - 4) + 2) between the vertical lines x = 1.1 and x = 1.4. Round to 1 decim... | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((1(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 2)/(-3(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 3))^2 + 3((1(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 2)/(-3(3e^(1(-5(-1(4x + 3) - 4) - 4))) - 3)) - 4, g(x) = 3cos(2π(3((-2(-1(-5x - 5) + 5) - 3)/(-2(-1(-5x - 5) + 5)... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(-2e^(-2((-2(1(-1|((-3x + 3)/(3x - 2)) - 1| + 2)^2 + 3(-1|((-3x + 3)/(3x - 2)) - 1| + 2) - 1) - 3)/(-2(1(-1|((-3x + 3)/(3x - 2)) - 1| + 2)^2 + 3(-1|((-3x + 3)/(3x - 2)) - 1| + 2) - 1) - 1))))^2 + 2(-2e^(-2((-2(1(-1|((-3x + 3)/(3x - 2)) - 1... | 1.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-4(-1sin(2π((1(-3|(-1x - 4) + 2| + 3))/(3(-3|(-1x - 4) + 2| + 3) + 2)) - 2)) + 4)^2 + 1(-4(-1sin(2π((1(-3|(-1x - 4) + 2| + 3))/(3(-3|(-1x - 4) + 2| + 3) + 2)) - 2)) + 4) + 2, g(x) = (-2((1(-4(-4(-2x + 4)^2 - 2(-2x + 4) + 3)^2 - 5(-4(-2x +... | 5.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((1(2sin(1π(4((-2(-4x) - 1)/(-3(-4x)))^2 + 5((-2(-4x) - 1)/(-3(-4x))) + 1)) - 3) + 3)/(-1(2sin(1π(4((-2(-4x) - 1)/(-3(-4x)))^2 + 5((-2(-4x) - 1)/(-3(-4x))) + 1)) - 3) - 1)) and g(x) = (-1((1(2e^(1(-1(-3x^2 + 5x)^2 + 2(-3x^2 + 5x) - 4)) + 1... | 30.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(4(-2|((-1(-1|(3|x + 3| - 3) + 3| + 1) + 3)/(2(-1|(3|x + 3| - 3) + 3| + 1) - 1)) + 1| - 3)^2 - 3) - 4, g(x) = 2|(5((1(5((3x)/(-1x + 2)) - 3) - 3)/(-2(5((3x)/(-1x + 2)) - 3) - 3)) + 3) - 1| + 1, x = 0.2, and x = 0.30000000000000004. Round yo... | 10.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-1((1(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5) + 2)/(2(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5)))^2 - 2((1(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5) + 2)/(2(-2((-2(5x - 2) + 2)/(-2(5x - 2) - 3)) + 5))) + 1) - 1| - 3 and g(x) = 2|((-3... | -0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2((-2(-1(-2e^(-1(-1|(-4x^2 - 5x + 1)|)))) - 3)/(1(-1(-2e^(-1(-1|(-4x^2 - 5x + 1)|)))) - 2)) + 1 and g(x) = -1|(2sin(3π((2((-3((-2x - 1)/(-2x + 3)) + 1)/(-1((-2x - 1)/(-2x + 3)) - 2)) + 1)/(1((-3((-2x - 1)/(-2x + 3)) + 1)/(-1((-2x - 1)/(-2x +... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(1((1((3(-3(2sin(3πx - 1) - 1) - 2) - 3)/(-1(-3(2sin(3πx - 1) - 1) - 2) + 2)) + 3)/(-2((3(-3(2sin(3πx - 1) - 1) - 2) - 3)/(-1(-3(2sin(3πx - 1) - 1) - 2) + 2)) + 1)) - 2) + 1| - 3 and g(x) = -1((-2(-1e^(-1(-4(2x - 3) + 2)) + 1) + 3)/(-2(-1... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1|(-2cos(1π((2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)) - 1)/(-2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)))) + 3) - 1) - 2|)^2 + 3(1|(-2cos(1π((2((-3(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5) + 1)) - 1)/(-2((-3(-5x... | 3.0 | MATH |
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