{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3((-3(-2sin(1\u03c0x - 2) + 2) + 2)/(2(-2sin(1\u03c0x - 2) + 2) + 1)) + 1)/(-2((-3(-2sin(1\u03c0x - 2) + 2) + 2)/(2(-2sin(1\u03c0x - 2) + 2) + 1)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2(2e^(2(1|x + 2| + 2)))^2 + 2(2e^(2(1|x + 2| + 2))) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2|(-1(-1sin(2\u03c0x - 2) - 2) - 4) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 5((-2(3x - 4) + 1)/(-1(3x - 4) + 3))^2 + 4((-2(3x - 4) + 1)/(-1(3x - 4) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3e^(-2(-3|((2x - 2)/(3x - 1)) - 3| - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-1(-3x)^2 + 5(-3x) - 1) + 2)/(2(-1(-3x)^2 + 5(-3x) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(2e^(2((-2x)/(1x + 2))) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2(-1(-1sin(1\u03c0x - 2) + 1) + 5) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2cos(2\u03c0(-1|(2|x - 1| + 1) - 2| + 1) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3sin(2\u03c0(5(2|x + 2| + 3)^2 + 1(2|x + 2| + 3) + 4)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(5(2|x - 2| - 3)^2 + 3(2|x - 2| - 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 5(-3(-5x^2 - 1x + 3)^2 + 3(-5x^2 - 1x + 3) - 4)^2 - 1(-3(-5x^2 - 1x + 3)^2 + 3(-5x^2 - 1x + 3) - 4) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5(-3sin(3\u03c0(1|x - 3| + 1) - 1)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2sin(3\u03c0((3(-4x^2 + 2x - 4) + 1)/(3(-4x^2 + 2x - 4) - 2))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2|(-2sin(1\u03c0((1x + 1)/(-2x + 1)) - 3) + 2) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(-2(-1|x - 2|)^2 + 3(-1|x - 2|) - 3) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -5(1cos(2\u03c0(-4x^2 - 4x + 5)))^2 + 5(1cos(2\u03c0(-4x^2 - 4x + 5))) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3((-2(3cos(1\u03c0x - 2) - 2) + 1)/(-1(3cos(1\u03c0x - 2) - 2))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(3cos(1\u03c0(-5x^2 + 5x + 3) - 3) + 3)^2 - 3(3cos(1\u03c0(-5x^2 + 5x + 3) - 3) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(1\u03c0(2((-2x)/(-1x + 3)) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3|(1e^(2(-5x^2 + 4x + 2)) - 2) - 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -4(2(3|x + 3| - 3)^2 + 4(3|x + 3| - 3) + 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1e^(2(2|x - 2| + 3))) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2cos(3\u03c0(3|(-1|x + 1| + 3) + 3| - 1) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-3sin(3\u03c0(1|x + 1| - 3)) - 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4((2(3x^2 - 3x - 2) + 2)/(2(3x^2 - 3x - 2) - 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(2sin(3\u03c0((2x + 2)/(1x - 2)))) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3cos(2\u03c0((-2(3|x - 2| + 1) + 1)/(-2(3|x - 2| + 1) + 3)) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(2|(3x^2 + 2x - 3) - 3|) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1((2(-1x^2 + 2x - 4) - 1)/(-2(-1x^2 + 2x - 4) - 1)) - 1)/(1((2(-1x^2 + 2x - 4) - 1)/(-2(-1x^2 + 2x - 4) - 1)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -5(1sin(3\u03c0(-2x^2 - 4x + 1)))^2 - 2(1sin(3\u03c0(-2x^2 - 4x + 1))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2cos(3\u03c0(1(1x^2 + 2x - 5)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1(1x^2 - 1x + 1) - 4) + 2)/(1(-1(1x^2 - 1x + 1) - 4) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2e^(-1(3|(-5x^2 - 2x - 2) + 3| + 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3|(1|(3cos(2\u03c0x - 2) + 1) - 2| + 2) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3e^(2(1(4x + 5)^2 + 1(4x + 5) - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(-1e^(2(4x - 5))) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1((-1(-2x^2 - 1) - 1)/(1(-2x^2 - 1) + 2)) + 1)/(-3((-1(-2x^2 - 1) - 1)/(1(-2x^2 - 1) + 2)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(2(-1sin(3\u03c0x) + 2) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-1|(1x^2 - 1x - 1) + 2| - 3)^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1sin(1\u03c0(3(-1|x - 2| + 1) + 4) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-3(-3|x - 2| + 1) - 1) - 3)/(1(-3(-3|x - 2| + 1) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(2e^(1((3x - 3)/(1x))) - 1) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 4(-5(-3sin(3\u03c0x + 2) + 2)^2 - 3(-3sin(3\u03c0x + 2) + 2) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(-1e^(-2(-2x^2 + 5x - 2)) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1(-5(2sin(3\u03c0x) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2e^(1(1|(3|x - 3| + 2) - 2| + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1e^(2(-2|((3x - 2)/(-3x - 3)) - 3| - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2((3(-1x^2 + 5x + 1) + 3)/(1(-1x^2 + 5x + 1) - 3)) - 1)/(-1((3(-1x^2 + 5x + 1) + 3)/(1(-1x^2 + 5x + 1) - 3)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(-1(3|x + 3| - 2) + 3) - 1)/(2(-1(3|x + 3| - 2) + 3) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2e^(-2(1(3x^2 - 5x + 3) - 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3((3(1cos(3\u03c0x - 1)))/(-1(1cos(3\u03c0x - 1)))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4(-5(-1sin(3\u03c0x - 1) + 3)^2 - 1(-1sin(3\u03c0x - 1) + 3) - 1)^2 + 4(-5(-1sin(3\u03c0x - 1) + 3)^2 - 1(-1sin(3\u03c0x - 1) + 3) - 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(2|(1x^2 + 3x + 3) + 1| + 3) + 2)/(-2(2|(1x^2 + 3x + 3) + 1| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2cos(2\u03c0(5(2x^2 + 1x + 1) + 5) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1((3(5x^2 - 4x) + 2)/(3(5x^2 - 4x) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2(5(4x^2 - 4x - 2)^2 + 5(4x^2 - 4x - 2) - 1)^2 - 4(5(4x^2 - 4x - 2)^2 + 5(4x^2 - 4x - 2) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1((-3((-3x - 3)/(-1x + 3)) - 1)/(-1((-3x - 3)/(-1x + 3)) - 1))^2 - 3((-3((-3x - 3)/(-1x + 3)) - 1)/(-1((-3x - 3)/(-1x + 3)) - 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(4(-3x^2 - 3x - 4)^2 + 1(-3x^2 - 3x - 4) + 4) - 2)/(-1(4(-3x^2 - 3x - 4)^2 + 1(-3x^2 - 3x - 4) + 4) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-3((1(1x^2 + 4x) - 1)/(2(1x^2 + 4x) - 1)) + 3)/(2((1(1x^2 + 4x) - 1)/(2(1x^2 + 4x) - 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(3e^(-1(1|x - 2|)) + 1)^2 + 5(3e^(-1(1|x - 2|)) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3((-2(2cos(2\u03c0x + 3) - 3) - 2)/(3(2cos(2\u03c0x + 3) - 3) - 2)) + 2)/(2((-2(2cos(2\u03c0x + 3) - 3) - 2)/(3(2cos(2\u03c0x + 3) - 3) - 2)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(5(5x^2 - 4)^2 - 2(5x^2 - 4) + 2) + 1)/(1(5(5x^2 - 4)^2 - 2(5x^2 - 4) + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(2sin(3\u03c0(1x^2 + 2x) + 2) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2(1cos(1\u03c0(3|x| + 1) + 2) - 1)^2 + 2(1cos(1\u03c0(3|x| + 1) + 2) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2((-2(-3e^(1x) - 1) - 3)/(3(-3e^(1x) - 1) + 3))^2 - 4((-2(-3e^(1x) - 1) - 3)/(3(-3e^(1x) - 1) + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|(-2sin(1\u03c0(-3x + 4) + 3) + 3) + 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2sin(2\u03c0(1|(3|x - 3| - 2) + 1| - 3) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2e^(2(-1|((1x + 1)/(1x - 3)) - 1| - 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1(-4(-2sin(2\u03c0x + 2)) - 4)^2 - 4(-4(-2sin(2\u03c0x + 2)) - 4) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(2|((1x + 3)/(2x)) + 3| - 1) + 2)/(-1(2|((1x + 3)/(2x)) + 3| - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1(1x^2 + 5) - 5) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5((3((3x)/(3x + 1)) + 3)/(1((3x)/(3x + 1)) + 1))^2 + 5((3((3x)/(3x + 1)) + 3)/(1((3x)/(3x + 1)) + 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2((-1(-1x^2 - 1x) - 3)/(-2(-1x^2 - 1x) + 3)) + 1)/(2((-1(-1x^2 - 1x) - 3)/(-2(-1x^2 - 1x) + 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(2e^(1(-4x^2 + 3x - 2)) - 1) - 1)/(-1(2e^(1(-4x^2 + 3x - 2)) - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2sin(2\u03c0(-4((3x + 1)/(-3x + 2)) - 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2e^(-1(1|((-2x - 1)/(2x + 2))| + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1sin(1\u03c0(-1(-2|x - 3| - 2) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(3sin(2\u03c0((1x + 1)/(3x + 2)) - 3)) + 2)/(-3(3sin(2\u03c0((1x + 1)/(3x + 2)) - 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(1|(1cos(2\u03c0x + 2) + 2) + 3|) - 1)/(-2(1|(1cos(2\u03c0x + 2) + 2) + 3|) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((1((3x - 3)/(-2x)))/(1((3x - 3)/(-2x)) - 3))^2 - 1((1((3x - 3)/(-2x)))/(1((3x - 3)/(-2x)) - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3sin(1\u03c0((-2((-1x - 2)/(-2x + 1)) + 3)/(3((-1x - 2)/(-2x + 1)) + 2)) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2cos(2\u03c0((2(2|x + 3| + 1) - 2)/(-3(2|x + 3| + 1) - 2))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(-3|(2cos(2\u03c0x + 2) + 1) - 3| + 2)^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2sin(2\u03c0(3(-4x^2 + 3x + 3) - 5) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(-2(3cos(3\u03c0x + 3)) + 3) - 1)/(3(-2(3cos(3\u03c0x + 3)) + 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3(1sin(3\u03c0(-1x^2 - 5x + 5) - 3) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2|(-2cos(2\u03c0(3|x| - 3) - 1) - 3)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 4(2(2sin(1\u03c0x + 3) + 2) + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(1|(3x + 4)| - 3)^2 - 2(1|(3x + 4)| - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(4(-3sin(1\u03c0x + 3))^2 + 3(-3sin(1\u03c0x + 3)) - 5)^2 + 3(4(-3sin(1\u03c0x + 3))^2 + 3(-3sin(1\u03c0x + 3)) - 5) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2|(4(4x^2 - 2)^2 + 1(4x^2 - 2) - 3) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(2e^(1(1x^2 + 2x - 5)) - 1)^2 - 5(2e^(1(1x^2 + 2x - 5)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(2|(5x^2 + 2x + 2) + 2| + 3)^2 - 4(2|(5x^2 + 2x + 2) + 2| + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2(-3cos(2\u03c0((3x + 2)/(-1x - 1)))))/(1(-3cos(2\u03c0((3x + 2)/(-1x - 1)))) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-4((3x - 3)/(2x)) + 1) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 4(-1(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 2)^2 + 1(-1(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-5(1x^2 - 1x + 5)^2 - 4(1x^2 - 1x + 5) + 5)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(2(-2cos(3\u03c0x - 1) + 2)^2 - 2(-2cos(3\u03c0x - 1) + 2) - 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1(1|(5x^2 - 4) - 1| - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -5(-2cos(1\u03c0(-3|x + 2| + 3) + 3))^2 + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3(-2sin(3\u03c0((2x + 2)/(1x)) + 2) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(2sin(1\u03c0((-1x - 2)/(-2x - 1)) - 1) + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-2e^(1((1x + 2)/(-1x))) - 1) + 2)/(-3(-2e^(1((1x + 2)/(-1x))) - 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-3(-2|x + 1| + 1)^2) + 3)/(-1(-3(-2|x + 1| + 1)^2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3cos(3\u03c0((-3((-3x - 1)/(-1x - 2)) - 3)/(-1((-3x - 1)/(-1x - 2))))) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (1(1e^(1(-5x^2 - 1x + 2)) - 1) - 3)/(3(1e^(1(-5x^2 - 1x + 2)) - 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(1((3x)/(-1x - 3)) - 5)^2 + 3(1((3x)/(-1x - 3)) - 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-2|(1cos(2\u03c0x + 3) - 2) - 1| + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(-3(3sin(2\u03c0x + 1))^2 + 4(3sin(2\u03c0x + 1)) + 3) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|((1(1cos(2\u03c0x + 1) + 3) + 1)/(1(1cos(2\u03c0x + 1) + 3))) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3|(1|(5x^2 - 5x + 4) - 2| + 3) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1sin(3\u03c0(1(1x - 3)^2 - 2(1x - 3) + 1)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "503", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-1((-1x + 1)/(3x + 2))^2 - 1((-1x + 1)/(3x + 2)) - 4) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2(-4(1sin(3\u03c0x - 1) - 2)^2 + 4(1sin(3\u03c0x - 1) - 2) + 4)^2 - 2(-4(1sin(3\u03c0x - 1) - 2)^2 + 4(1sin(3\u03c0x - 1) - 2) + 4) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3e^(-1((2(-3|x| - 1))/(-3(-3|x| - 1) + 2))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 5((2(-1cos(2\u03c0x - 1) - 1) - 3)/(3(-1cos(2\u03c0x - 1) - 1) - 2))^2 + 4((2(-1cos(2\u03c0x - 1) - 1) - 3)/(3(-1cos(2\u03c0x - 1) - 1) - 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(3sin(2\u03c0(-5x + 1) - 2) + 2) - 1)/(-3(3sin(2\u03c0(-5x + 1) - 2) + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(-3(2cos(3\u03c0x + 1))^2 + 3(2cos(3\u03c0x + 1)) + 2)^2 - 2(-3(2cos(3\u03c0x + 1))^2 + 3(2cos(3\u03c0x + 1)) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(3|(-3x^2 - 5x) + 1| + 1) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2(-3|(-4x^2 + 1x + 5) + 2| - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4((-1(2x - 1) - 1)/(1(2x - 1) + 2))^2 - 5((-1(2x - 1) - 1)/(1(2x - 1) + 2)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3|(-2(3x^2 + 5x - 2)^2 + 5(3x^2 + 5x - 2) + 4) - 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2cos(2\u03c0(-3|(2x + 4) - 1|) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3e^(1(-4(-5x^2 + 1x)^2 + 3(-5x^2 + 1x) - 5)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2(1((3x + 2)/(2x + 2))^2 + 1)^2 + 1(1((3x + 2)/(2x + 2))^2 + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3(-2(1cos(2\u03c0x + 3) - 2)^2 + 2(1cos(2\u03c0x + 3) - 2))^2 - 1(-2(1cos(2\u03c0x + 3) - 2)^2 + 2(1cos(2\u03c0x + 3) - 2)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2(-3e^(2(-2|x + 2| - 3)) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3|(1sin(1\u03c0(1x^2 + 2x - 2) + 3) + 3) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(2|(1e^(2x) + 3) - 3| - 1)^2 - 1(2|(1e^(2x) + 3) - 3| - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (2(-3(-3cos(3\u03c0x + 1) + 2)^2 + 5(-3cos(3\u03c0x + 1) + 2) + 5) - 3)/(-1(-3(-3cos(3\u03c0x + 1) + 2)^2 + 5(-3cos(3\u03c0x + 1) + 2) + 5) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1(1x^2 - 3x - 1)^2 - 3(1x^2 - 3x - 1) + 3) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1cos(2\u03c0(3(1x + 3) - 3) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2sin(1\u03c0(1(2x - 2) - 5) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(-1e^(1(1x^2 - 2x + 3))) + 2)/(-1(-1e^(1(1x^2 - 2x + 3))) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(2(-1cos(2\u03c0x + 2) + 2)^2 + 2(-1cos(2\u03c0x + 2) + 2) - 3)^2 - 3(2(-1cos(2\u03c0x + 2) + 2)^2 + 2(-1cos(2\u03c0x + 2) + 2) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3e^(-1(-5(3|x - 2| - 3)^2 + 1(3|x - 2| - 3) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 5(5(-1sin(1\u03c0x + 1) + 2)^2 + 4(-1sin(1\u03c0x + 1) + 2) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3sin(2\u03c0(3(-2|x + 2| + 1) - 1) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1((2(2sin(1\u03c0x + 2) - 3) - 2)/(-3(2sin(1\u03c0x + 2) - 3))) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3e^(-1(2((-2x + 3)/(2x + 1))^2 - 1((-2x + 3)/(2x + 1)) - 5)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (1(-1sin(1\u03c0(1x - 4) + 1) - 2) + 3)/(3(-1sin(1\u03c0(1x - 4) + 1) - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(-1(3sin(2\u03c0x - 3) + 2)^2 + 2(3sin(2\u03c0x - 3) + 2) + 2)^2 + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1(-2(-3e^(2x) - 1)^2 - 4(-3e^(2x) - 1) - 4)^2 - 3(-2(-3e^(2x) - 1)^2 - 4(-3e^(2x) - 1) - 4) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4(-4(1sin(3\u03c0x + 1)) - 5)^2 + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(-1|(1|x - 3| - 2)| - 1)^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(2e^(1((2x + 3)/(1x - 3))) + 2))/(3(2e^(1((2x + 3)/(1x - 3))) + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(-2|(-3x^2 + 5x - 1) + 1| + 2) - 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (1(3|(1cos(2\u03c0x + 1) + 1) - 2|) - 3)/(3(3|(1cos(2\u03c0x + 1) + 1) - 2|) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1sin(3\u03c0(4(-3x + 5) - 5) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3|(-3|(-1cos(2\u03c0x - 3)) + 1|) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(-3|((-1x + 1)/(1x))| + 2)| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-4((-3x + 3)/(-1x + 2))^2 + 5((-3x + 3)/(-1x + 2)) - 3)^2 + 3(-4((-3x + 3)/(-1x + 2))^2 + 5((-3x + 3)/(-1x + 2)) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(-2|(-1cos(2\u03c0x + 2) - 2) - 2| + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-1(-2cos(3\u03c0x - 2) - 2) - 4)^2 - 4(-1(-2cos(3\u03c0x - 2) - 2) - 4) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2e^(-1(-4(-4x^2 - 2x - 1)^2 - 3(-4x^2 - 2x - 1))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(-2|(4x^2 + 1x + 1)| + 2) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3|(1cos(1\u03c0(-3x^2 + 2) + 3) - 1)| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (3(-2sin(2\u03c0((-1x - 2)/(1x)) + 1) + 2) + 3)/(-2(-2sin(2\u03c0((-1x - 2)/(1x)) + 1) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(3(3|x - 2|)^2 - 2(3|x - 2|) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2(-2sin(3\u03c0(-1x + 5) + 3) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(-1(-2e^(2x) + 2)^2 + 5(-2e^(2x) + 2) + 1)^2 + 2(-1(-2e^(2x) + 2)^2 + 5(-2e^(2x) + 2) + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|(-1|(2cos(2\u03c0x)) - 1| - 3) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-1|((3x - 3)/(3x + 1))| + 3)^2 + 2(-1|((3x - 3)/(3x + 1))| + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(1(-4x + 5)^2 - 4(-4x + 5)) + 2)/(-2(1(-4x + 5)^2 - 4(-4x + 5)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(-1sin(3\u03c0((1x + 2)/(-2x)) - 2) + 2) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -5(1sin(3\u03c0(-2|x - 1| + 1) + 1) - 1)^2 + 5(1sin(3\u03c0(-2|x - 1| + 1) + 1) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3((2(2cos(3\u03c0x + 1) + 3) + 2)/(-2(2cos(3\u03c0x + 1) + 3) + 3)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3sin(3\u03c0(1|(-5x - 3) - 1| + 1) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(3|(-5x)| - 1) - 3)/(-1(3|(-5x)| - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-3(-3cos(2\u03c0x + 3) + 1))^2 - 1(-3(-3cos(2\u03c0x + 3) + 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(-3sin(2\u03c0(-5x^2 - 5x - 2) - 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(1(-2x + 1)^2 - 4(-2x + 1) + 4) - 3)/(1(1(-2x + 1)^2 - 4(-2x + 1) + 4) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(1sin(2\u03c0(1x - 4) - 1) - 3))/(-3(1sin(2\u03c0(1x - 4) - 1) - 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3cos(3\u03c0(-5((1x - 1)/(2x + 3)))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-2|(3x^2 - 2x + 1) + 2| + 2)^2 - 4(-2|(3x^2 - 2x + 1) + 2| + 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-1|((-2x - 1)/(-1x + 3)) - 3|)^2 + 2(-1|((-2x - 1)/(-1x + 3)) - 3|) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1|(2sin(2\u03c0(-3x^2 - 4x - 3)) - 3) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(3|(-4x^2 - 4x - 3) - 2| - 1) + 2)/(2(3|(-4x^2 - 4x - 3) - 2| - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3cos(3\u03c0(1(2|x + 2| - 1) + 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-3(-3|x| - 3)^2 - 4(-3|x| - 3) - 5) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1(4(2sin(3\u03c0x + 2) - 3) + 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(-1e^(-2((-3x + 3)/(3x + 3))) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(-1|(2cos(2\u03c0x + 1) + 1)| - 1) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3cos(1\u03c0((3(3x) + 1)/(-2(3x) - 2)) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(4(-1sin(1\u03c0x - 2) - 2)^2) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3e^(-2(2(3x^2 - 1x - 3) - 5)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (3(2e^(-1(-1x^2 - 3x)) + 3) + 3)/(-1(2e^(-1(-1x^2 - 3x)) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1(1(-3sin(2\u03c0x + 2) + 2)^2 + 4(-3sin(2\u03c0x + 2) + 2) - 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4((-2(5x) + 2)/(1(5x) + 2))^2 - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3|(2|(-2cos(1\u03c0x + 2) - 3) - 1|) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4(2(2|x - 1| - 3)^2 - 3(2|x - 1| - 3)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2e^(-2(-1|(2x - 5) + 2| - 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1e^(2(-2|(1x^2 + 2x + 1)|)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4(1sin(1\u03c0(-1|x - 2| - 3) - 1) + 1)^2 + 2(1sin(1\u03c0(-1|x - 2| - 3) - 1) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2((1((-3x - 1)/(-2x - 2)) + 2)/(-1((-3x - 1)/(-2x - 2)) - 1))^2 - 4((1((-3x - 1)/(-2x - 2)) + 2)/(-1((-3x - 1)/(-2x - 2)) - 1)) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(5((-1x - 3)/(-2x - 1))^2 + 5((-1x - 3)/(-2x - 1)) + 4) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -5(1|(3sin(3\u03c0x) + 3) + 2| + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3cos(3\u03c0(-5(-2x^2 - 2x - 3) + 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(1|(-3|x| + 1) - 3| - 1)| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(1|(1cos(2\u03c0x + 2)) - 1|) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(2|(-3e^(1x) - 1) + 2| - 3))/(-1(2|(-3e^(1x) - 1) + 2| - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(5(-1|x - 3|)^2 - 4(-1|x - 3|) - 2) - 1)/(2(5(-1|x - 3|)^2 - 4(-1|x - 3|) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2sin(1\u03c0(2(-2x - 5)^2 - 5(-2x - 5)) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3(2((2x - 3)/(-2x - 1))^2 + 4((2x - 3)/(-2x - 1)) + 2)^2 + 2(2((2x - 3)/(-2x - 1))^2 + 4((2x - 3)/(-2x - 1)) + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2|(-2sin(3\u03c0((2x - 2)/(-1x + 2)) - 3)) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1(1(2cos(3\u03c0x + 2) - 1) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(3(1|x + 3| - 3)^2 + 5(1|x + 3| - 3)) + 2)/(1(3(1|x + 3| - 3)^2 + 5(1|x + 3| - 3)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2cos(3\u03c0(-1(-1x^2 + 5x) - 1) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1((2(2sin(2\u03c0x + 2) - 2) - 3)/(2(2sin(2\u03c0x + 2) - 2))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(-3((2x + 3)/(1x + 3))^2 + 5((2x + 3)/(1x + 3))) - 3)/(-2(-3((2x + 3)/(1x + 3))^2 + 5((2x + 3)/(1x + 3))) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2((-2(1x^2 + 4x - 1))/(-3(1x^2 + 4x - 1) + 4)) + 1)/(1((-2(1x^2 + 4x - 1))/(-3(1x^2 + 4x - 1) + 4)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(-3|((3x + 2)/(1x)) - 3| + 3) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(-1(-5x + 2)^2 - 2(-5x + 2) - 3) + 3)/(-2(-1(-5x + 2)^2 - 2(-5x + 2) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(-1(-2sin(1\u03c0x + 3) - 3) - 1))/(2(-1(-2sin(1\u03c0x + 3) - 3) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5((-2(1x^2 - 5x - 2) + 2)/(-2(1x^2 - 5x - 2) - 2)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (2(1sin(1\u03c0(1|x - 3| + 1) + 1) - 3) - 3)/(2(1sin(1\u03c0(1|x - 3| + 1) + 1) - 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(-3(-3cos(3\u03c0x - 1)) - 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1((1(5x^2 + 3x - 1) + 1)/(2(5x^2 + 3x - 1) - 1))^2 - 4((1(5x^2 + 3x - 1) + 1)/(2(5x^2 + 3x - 1) - 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2cos(2\u03c0((3(-1|x - 1| - 2) - 1)/(3(-1|x - 1| - 2) + 1)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(-2e^(-2(2x)) - 3) - 3)/(-3(-2e^(-2(2x)) - 3) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(-4(3|x - 1| - 3)^2 - 1(3|x - 1| - 3) + 5)| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1(1(1cos(2\u03c0x + 2) - 3)^2 - 3(1cos(2\u03c0x + 2) - 3) - 4) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|((3(3|x| + 2) - 2)/(-3(3|x| + 2) - 2)) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1(-2|(3cos(3\u03c0x + 2)) - 1|) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(2e^(1(-1|x| - 1)) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1e^(-1((-2(3|x| + 3) - 3)/(3(3|x| + 3)))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3e^(1(2(-1|x + 3|)^2 + 4(-1|x + 3|) + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3|((-3(-4x^2 + 1x + 1) + 1)/(1(-4x^2 + 1x + 1) - 3)) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(2((2x + 2)/(-1x + 2))^2 - 4((2x + 2)/(-1x + 2)) - 4) + 2)/(-2(2((2x + 2)/(-1x + 2))^2 - 4((2x + 2)/(-1x + 2)) - 4) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2(-4(1|x + 2| - 2)^2 + 1(1|x + 2| - 2) - 2)^2 - 2(-4(1|x + 2| - 2)^2 + 1(1|x + 2| - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(2e^(2(3|x|)) + 1))/(-3(2e^(2(3|x|)) + 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|(4((1x + 3)/(-2x + 3))^2 - 3((1x + 3)/(-2x + 3)) - 3)| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(3(2|x - 2| - 2)^2 + 3(2|x - 2| - 2) + 5) + 2)/(-3(3(2|x - 2| - 2)^2 + 3(2|x - 2| - 2) + 5) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1((2x + 2)/(3x + 1))^2 + 1((2x + 2)/(3x + 1)) - 5)^2 - 4(-1((2x + 2)/(3x + 1))^2 + 1((2x + 2)/(3x + 1)) - 5) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(-2sin(2\u03c0((-2x - 1)/(3x + 3)) + 2) - 1) + 3)/(-3(-2sin(2\u03c0((-2x - 1)/(3x + 3)) + 2) - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3(3cos(1\u03c0(4x^2 + 5x + 3) + 2) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1|(-1(-2x^2 + 5x + 5)^2 - 2(-2x^2 + 5x + 5) - 1) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(1e^(-1(-2|x| - 1)) - 2) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(1|(-3|x + 2| - 1) + 3| + 3) + 1)/(3(1|(-3|x + 2| - 1) + 3| + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-1(2|(-3cos(2\u03c0x - 2) - 2) + 1| - 1) - 1)/(-2(2|(-3cos(2\u03c0x - 2) - 2) + 1| - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(-1|(-4x^2 + 5x) - 2| + 1) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(1cos(1\u03c0(-4x^2 - 3x + 3) + 2) - 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2((3(3x^2 + 1x + 5) - 3)/(2(3x^2 + 1x + 5) + 2)) - 3)/(1((3(3x^2 + 1x + 5) - 3)/(2(3x^2 + 1x + 5) + 2)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(2\u03c0((-2((1x - 3)/(1x + 3)) - 1)/(2((1x - 3)/(1x + 3))))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5(2(1|x + 3| - 1)^2 + 1(1|x + 3| - 1) + 1)^2 - 5(2(1|x + 3| - 1)^2 + 1(1|x + 3| - 1) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5((-2(3sin(3\u03c0x - 1) + 2) - 1)/(2(3sin(3\u03c0x - 1) + 2) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(3\u03c0(-2|(4x + 4) + 1| - 2) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(3\u03c0(-2(4x - 1) - 4) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((-3(-1x + 5) - 1)/(-3(-1x + 5) - 2))^2 + 2((-3(-1x + 5) - 1)/(-3(-1x + 5) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(-2e^(1((-3x - 1)/(1x - 3)))) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (3(-3|(-3x^2 + 5x + 4) - 3| - 1) + 3)/(-2(-3|(-3x^2 + 5x + 4) - 3| - 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(2cos(1\u03c0(5x^2 - 2x + 4) + 3) + 1)^2 + 2(2cos(1\u03c0(5x^2 - 2x + 4) + 3) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2e^(2(2|((2x)/(-3x - 3)) + 1| - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2cos(2\u03c0((-1(-4x^2 + 3x + 5) - 2)/(-2(-4x^2 + 3x + 5) - 2)) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(1|(2|x| - 2) + 2| + 2))/(-3(1|(2|x| - 2) + 2| + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(1e^(-2(-3x + 5)) + 1)^2 - 5(1e^(-2(-3x + 5)) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3(-2|(3|x| + 1) - 3| + 1)^2 + 4(-2|(3|x| + 1) - 3| + 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3((-1(-2e^(-1x)) - 3)/(-3(-2e^(-1x)) - 2))^2 + 3((-1(-2e^(-1x)) - 3)/(-3(-2e^(-1x)) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(2(-4((-2x + 3)/(1x + 1)) - 4)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1cos(2\u03c0(-1(-1|x - 3| - 3) + 4) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2e^(1(1((2x - 2)/(2x + 3))^2 - 4)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(4(3sin(2\u03c0x + 3) + 1) + 5) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-3(-1|(-3sin(1\u03c0x - 1) - 2) + 3| + 1) + 2)/(2(-1|(-3sin(1\u03c0x - 1) - 2) + 3| + 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(-2((3x + 1)/(1x + 1))^2 + 4((3x + 1)/(1x + 1)) - 3) - 3)/(-1(-2((3x + 1)/(1x + 1))^2 + 4((3x + 1)/(1x + 1)) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3(4(-1sin(3\u03c0x))^2 - 2(-1sin(3\u03c0x)) + 3) + 2)/(2(4(-1sin(3\u03c0x))^2 - 2(-1sin(3\u03c0x)) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1|(-4(1|x + 3| + 1)^2 + 3(1|x + 3| + 1) - 1) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(5(-2cos(3\u03c0x - 1) - 2)^2 - 2(-2cos(3\u03c0x - 1) - 2) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-3(-1(-2x^2 - 2x + 4)^2 - 4(-2x^2 - 2x + 4) - 4) + 2)/(2(-1(-2x^2 - 2x + 4)^2 - 4(-2x^2 - 2x + 4) - 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(3(1cos(2\u03c0x - 2) + 3) - 1) + 3)/(1(3(1cos(2\u03c0x - 2) + 3) - 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(5(1|x + 1|)^2 - 3(1|x + 1|) + 2) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1|((-3x + 2)/(-2x)) + 3| - 1) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(1|(-3x^2 + 4x - 3) - 2| - 2)^2 - 1(1|(-3x^2 + 4x - 3) - 2| - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(2((-2x + 3)/(2x - 1)) - 5)^2 + 1(2((-2x + 3)/(2x - 1)) - 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -4(4(-1|x - 1| + 3)^2 - 5(-1|x - 1| + 3) + 1)^2 - 3(4(-1|x - 1| + 3)^2 - 5(-1|x - 1| + 3) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-1(3((1x - 1)/(-1x - 1))^2 + 3((1x - 1)/(-1x - 1)) - 1) - 3)/(-2(3((1x - 1)/(-1x - 1))^2 + 3((1x - 1)/(-1x - 1)) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(-1e^(2(3|x + 1| - 1))) + 2)/(-2(-1e^(2(3|x + 1| - 1)))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1cos(2\u03c0(1|(1x - 1) - 2|) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-3(-2|x - 3| - 3)^2 - 2(-2|x - 3| - 3) + 5)^2 - 4(-3(-2|x - 3| - 3)^2 - 2(-2|x - 3| - 3) + 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3(-5(-3|x| + 1)^2 - 5(-3|x| + 1) + 1)^2 - 4(-5(-3|x| + 1)^2 - 5(-3|x| + 1) + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3((-1(-1sin(1\u03c0x - 2) + 2))/(2(-1sin(1\u03c0x - 2) + 2) - 1))^2 + 3((-1(-1sin(1\u03c0x - 2) + 2))/(2(-1sin(1\u03c0x - 2) + 2) - 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-1((1x + 2)/(2x + 1))^2 + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(-1|(1x^2 - 1x - 3) + 3| - 3) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5((-1(-2sin(2\u03c0x + 1)) - 2)/(2(-2sin(2\u03c0x + 1)) + 2))^2 + 1((-1(-2sin(2\u03c0x + 1)) - 2)/(2(-2sin(2\u03c0x + 1)) + 2)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(3cos(3\u03c0(3x + 4) + 2) - 1)^2 + 5(3cos(3\u03c0(3x + 4) + 2) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1sin(2\u03c0((1((-1x - 3)/(2x)))/(-1((-1x - 3)/(2x)) + 2)) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2e^(-2((2((-3x - 1)/(-1x - 2)))/(2((-3x - 1)/(-1x - 2)) - 3))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(2(1x - 1)^2 + 2) + 3)/(-3(2(1x - 1)^2 + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1((-2(-3sin(3\u03c0x) - 2) + 3)/(-1(-3sin(3\u03c0x) - 2) + 3))^2 - 5((-2(-3sin(3\u03c0x) - 2) + 3)/(-1(-3sin(3\u03c0x) - 2) + 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(3(2|x - 2| - 3)^2 + 3(2|x - 2| - 3) - 4))/(2(3(2|x - 2| - 3)^2 + 3(2|x - 2| - 3) - 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3e^(1(-3((-2x + 2)/(1x - 3))^2 - 1((-2x + 2)/(1x - 3)) + 4)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -4(-2|(-5x^2 + 5) - 2| + 1)^2 - 3(-2|(-5x^2 + 5) - 2| + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(-3|((3x)/(2x - 1)) - 2|) + 2)/(-2(-3|((3x)/(2x - 1)) - 2|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(2(3x^2 - 1x + 3) - 2) - 2)/(1(2(3x^2 - 1x + 3) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(1|(1e^(-2x) - 3) - 2| - 3)^2 - 3(1|(1e^(-2x) - 3) - 2| - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(1sin(3\u03c0(-4x - 5) + 3)))/(1(1sin(3\u03c0(-4x - 5) + 3)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2|(-4(-2|x - 1| + 2)^2 - 5(-2|x - 1| + 2) - 2)| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(-5(3cos(2\u03c0x + 3) + 2) + 4)^2 + 3(-5(3cos(2\u03c0x + 3) + 2) + 4) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|(4(5x^2 - 3x + 3)^2 + 2(5x^2 - 3x + 3)) - 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(3\u03c0(-5(-2x^2 - 2x) - 1) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1(4(-2sin(1\u03c0x - 1) - 1)^2 - 2(-2sin(1\u03c0x - 1) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|(1(2|x + 3| + 2)^2 - 3(2|x + 3| + 2) + 2) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1|(-2sin(2\u03c0(5x + 5) + 1) - 3) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3sin(2\u03c0(-1|((-2x - 2)/(1x + 3)) + 2| - 1) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2|(2|x - 3| + 2) - 3| - 2)^2 + 3(-2|(2|x - 3| + 2) - 3| - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2cos(1\u03c0(2(1|x - 3| + 3)^2 + 4(1|x - 3| + 3) - 3) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(3sin(2\u03c0(-2x^2 + 4x - 3) - 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1cos(3\u03c0(-1(-2x^2 + 3x + 3) + 3) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2cos(1\u03c0(-1|(-1x^2 - 2x + 4) + 3|) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-2|((-1x + 3)/(2x))| + 1) - 3)/(-1(-2|((-1x + 3)/(2x))| + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1sin(2\u03c0(-2((1x + 2)/(-3x - 3))^2 + 3((1x + 2)/(-3x - 3)) - 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1cos(3\u03c0((-1(1|x - 1| - 1) - 2)/(2(1|x - 1| - 1) - 1)) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(2sin(2\u03c0((2x - 3)/(3x - 1))) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2sin(3\u03c0(1|((3x + 1)/(1x)) - 1| + 1) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2sin(1\u03c0(1(1x^2 - 5x - 1)^2 - 2(1x^2 - 5x - 1) + 5) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(2|(3|x| - 2) - 3| - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2((-3(1x^2 - 1x + 4) + 2)/(1(1x^2 - 1x + 4) - 2))^2 + 5((-3(1x^2 - 1x + 4) + 2)/(1(1x^2 - 1x + 4) - 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2|(-3sin(1\u03c0(2|x + 1|)) + 1) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-3|((2x + 2)/(-3x - 3)) - 2|) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(1(1x + 3)^2 - 5(1x + 3) - 3) - 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2sin(1\u03c0(2((1x - 1)/(2x + 3)) - 1) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(-5(-2|x - 1| + 1)^2 - 2(-2|x - 1| + 1) + 3) - 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3sin(1\u03c0(-5(5x) - 3) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1((-1(-3cos(1\u03c0x + 3) - 1) - 1)/(-2(-3cos(1\u03c0x + 3) - 1) + 3))^2 + 3((-1(-3cos(1\u03c0x + 3) - 1) - 1)/(-2(-3cos(1\u03c0x + 3) - 1) + 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3|((-2(-1sin(3\u03c0x) + 1) + 2)/(-2(-1sin(3\u03c0x) + 1) + 1)) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3(4(1cos(2\u03c0x + 1) + 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(2|(4x - 2) + 1| - 2)^2 - 4(2|(4x - 2) + 1| - 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(-1(3sin(2\u03c0x - 3) - 2)^2 - 5(3sin(2\u03c0x - 3) - 2)) + 1)/(1(-1(3sin(2\u03c0x - 3) - 2)^2 - 5(3sin(2\u03c0x - 3) - 2))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-4(2cos(1\u03c0x - 1)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-2(3e^(-1(-4x^2 - 5)) - 3) + 3)/(-1(3e^(-1(-4x^2 - 5)) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -5(2|(-4x + 3) + 2| - 2)^2 + 2(2|(-4x + 3) + 2| - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3(-1sin(2\u03c0(5x^2 + 4x - 4) - 3) - 3)^2 + 5(-1sin(2\u03c0(5x^2 + 4x - 4) - 3) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1((1(-1x^2 - 3x - 1) - 2)/(-2(-1x^2 - 3x - 1) - 3))^2 + 4((1(-1x^2 - 3x - 1) - 2)/(-2(-1x^2 - 3x - 1) - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2sin(1\u03c0((-3(5x - 5))/(-3(5x - 5) - 3)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(3((1x - 3)/(-2x - 1))^2 + 5((1x - 3)/(-2x - 1)) - 4) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (1((-1((1x - 2)/(2x - 3)) - 2)/(3((1x - 2)/(2x - 3)) + 2)))/(3((-1((1x - 2)/(2x - 3)) - 2)/(3((1x - 2)/(2x - 3)) + 2))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3(1sin(3\u03c0(4x^2 + 2x - 4)) - 1)^2 - 4(1sin(3\u03c0(4x^2 + 2x - 4)) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2sin(2\u03c0(-5((1x + 3)/(2x + 3))^2 - 3((1x + 3)/(2x + 3)) + 5) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3((-3(-3|x + 1| + 1) - 3)/(2(-3|x + 1| + 1) + 1)) - 1)/(-3((-3(-3|x + 1| + 1) - 3)/(2(-3|x + 1| + 1) + 1)) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2(2|(2sin(2\u03c0x + 2))| + 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3((-2(3sin(2\u03c0x + 3)) - 1)/(3(3sin(2\u03c0x + 3)) + 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-3(2sin(2\u03c0x - 2) - 3)^2 + 5(2sin(2\u03c0x - 2) - 3) + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 4(-2|(1cos(2\u03c0x) - 1) + 2|) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-3(3sin(3\u03c0(5x^2 + 5x + 3) - 1) + 1) - 1)/(1(3sin(3\u03c0(5x^2 + 5x + 3) - 1) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3((1(4x) + 3)/(-1(4x) - 1))^2 - 5((1(4x) + 3)/(-1(4x) - 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(3cos(2\u03c0(-2|x - 1| - 3) - 1) - 2) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3e^(1(4(-4x - 3)^2 - 3(-4x - 3) + 2)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-1e^(-2((-2x + 1)/(2x + 3))) + 2) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1((1(1sin(2\u03c0x + 2) + 3) - 2)/(2(1sin(2\u03c0x + 2) + 3)))^2 - 3((1(1sin(2\u03c0x + 2) + 3) - 2)/(2(1sin(2\u03c0x + 2) + 3))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2|((2(5x^2 + 3) - 3)/(-3(5x^2 + 3) + 1)) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2sin(2\u03c0((-3(-4x + 3) + 2)/(1(-4x + 3) - 2)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-3sin(1\u03c0((1x + 2)/(-3x + 2)) + 3) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1(1sin(2\u03c0((-1x - 1)/(-2x + 3)) + 2) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2(-3(-3cos(2\u03c0x + 3) - 1)^2 + 2(-3cos(2\u03c0x + 3) - 1) - 4) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -4(-2e^(2(-3x^2 + 3x + 1)) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2sin(3\u03c0(-2|((1x + 2)/(-1x + 3))| - 2) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1e^(1(1((2x - 3)/(1x + 1)) + 5)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(-1(-3cos(2\u03c0x + 3) + 3) + 5) - 2)/(1(-1(-3cos(2\u03c0x + 3) + 3) + 5) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(1(-3|x - 2| + 2)^2 - 4(-3|x - 2| + 2) + 5) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (3(1e^(1(2|x + 3| + 3)) + 1) + 3)/(-2(1e^(1(2|x + 3| + 3)) + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3sin(1\u03c0((-2((-2x)/(1x - 3)) + 2)/(2((-2x)/(1x - 3)) - 1)) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(-3|(4x^2 - 4x - 4)| + 1) + 1)/(-2(-3|(4x^2 - 4x - 4)| + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(1|(-1x^2 + 5x + 4) + 2| - 1)^2 - 5(1|(-1x^2 + 5x + 4) + 2| - 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3sin(3\u03c0((-3(-3x^2 - 5x + 2) - 3)/(-3(-3x^2 - 5x + 2) - 2)) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(-2e^(2(5x^2 - 1x)) - 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2(1cos(3\u03c0((-3x - 2)/(2x)) - 1))^2 + 5(1cos(3\u03c0((-3x - 2)/(2x)) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-2(-1|(-3x^2 - 2x + 4)| - 1))/(2(-1|(-3x^2 - 2x + 4)| - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2|(1e^(1(-3|x| + 3)) + 3) - 1| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4((2(2|x| + 2) - 3)/(3(2|x| + 2) + 2))^2 + 1((2(2|x| + 2) - 3)/(3(2|x| + 2) + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(3|(2cos(3\u03c0x + 1) + 1) + 2| + 3) + 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 5(-2e^(2(-3x)) - 3)^2 + 2(-2e^(2(-3x)) - 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-5(1cos(3\u03c0x) - 1)^2 - 4(1cos(3\u03c0x) - 1))^2 + 2(-5(1cos(3\u03c0x) - 1)^2 - 4(1cos(3\u03c0x) - 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1cos(1\u03c0(-3|(-3x - 1) - 2| - 2) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-2|(2x^2 + 1) + 1| - 2) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1cos(3\u03c0(-3(1x - 5)^2 - 1) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(-3sin(2\u03c0(-3x^2 - 2x - 4) + 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(-2e^(1(5x^2)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3(-3(3sin(1\u03c0x) - 1) - 5) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(1e^(-1(-1|x + 3|))) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|(-2e^(-2(3|x - 3| - 1)) - 3) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1(2sin(2\u03c0x + 3))^2 - 3(2sin(2\u03c0x + 3)) + 1)^2 - 3(-1(2sin(2\u03c0x + 3))^2 - 3(2sin(2\u03c0x + 3)) + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (1((1(3sin(3\u03c0x - 1) - 3) + 3)/(-2(3sin(3\u03c0x - 1) - 3) - 3)))/(-2((1(3sin(3\u03c0x - 1) - 3) + 3)/(-2(3sin(3\u03c0x - 1) - 3) - 3)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2sin(1\u03c0(-1((-1x + 1)/(-2x + 3))^2 + 4((-1x + 1)/(-2x + 3)) - 1) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(2cos(2\u03c0((1x + 2)/(-1x + 2)) + 2) + 2) - 1)/(1(2cos(2\u03c0((1x + 2)/(-1x + 2)) + 2) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(2|(-3x^2 + 2) + 2| - 1) - 3)/(-1(2|(-3x^2 + 2) + 2| - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(3\u03c0(-1(1x + 1)^2 - 4(1x + 1) - 2) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3(1cos(2\u03c0(-4x^2 - 3x - 5) + 2) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3cos(2\u03c0(-4(-2|x + 3|) - 4) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3(-1sin(3\u03c0((-2x - 1)/(-3x - 3)) - 3) + 3) + 3)/(-3(-1sin(3\u03c0((-2x - 1)/(-3x - 3)) - 3) + 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1|(-1(-3sin(1\u03c0x - 2) + 3)^2 + 4(-3sin(1\u03c0x - 2) + 3)) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1(-1|(1cos(3\u03c0x - 3) - 3)| - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(1|(-2x + 3) - 3|) + 3)/(-3(1|(-2x + 3) - 3|) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(-3|(2|x| + 2)|) + 2)/(2(-3|(2|x| + 2)|) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 4(-1cos(1\u03c0(2|x + 2| - 3) - 1) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(1|((-1x + 3)/(2x + 3)) - 1| - 1) + 3)/(3(1|((-1x + 3)/(2x + 3)) - 1| - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1((-2(2x^2 + 3x - 1) + 3)/(-2(2x^2 + 3x - 1) - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3e^(-1(-4(-4x - 5)^2 + 2(-4x - 5) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1((1(3x^2 + 3) - 3)/(3(3x^2 + 3) - 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 5(-3cos(3\u03c0((-1x + 2)/(2x + 3)) + 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3(-1(1sin(1\u03c0x + 2) - 3)^2 - 4(1sin(1\u03c0x + 2) - 3))^2 - 5(-1(1sin(1\u03c0x + 2) - 3)^2 - 4(1sin(1\u03c0x + 2) - 3)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1cos(2\u03c0(-1|(1x^2 + 3x + 5) + 2| + 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1(2cos(1\u03c0((-1x + 1)/(-1x + 2)) + 2) + 3) - 3)/(1(2cos(1\u03c0((-1x + 1)/(-1x + 2)) + 2) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (1(1e^(2(2|x - 3| + 2)) + 3) + 3)/(3(1e^(2(2|x - 3| + 2)) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3(-1(3|x| - 1) + 5)^2 - 1(-1(3|x| - 1) + 5) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3(3sin(2\u03c0(-5x - 1) + 2) + 1)^2 + 5(3sin(2\u03c0(-5x - 1) + 2) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3sin(2\u03c0(1|(4x^2 - 1x - 4) - 2| + 2) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(3sin(3\u03c0(1x^2 + 4x + 1) + 2) - 2) - 2)/(-3(3sin(3\u03c0(1x^2 + 4x + 1) + 2) - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2e^(-1((-1(-2|x| - 1) - 3)/(3(-2|x| - 1) + 3))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(3\u03c0(-3(-1x - 4) - 2) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-3(-4x^2 + 1x)^2 + 1(-4x^2 + 1x) + 1)^2 - 2(-3(-4x^2 + 1x)^2 + 1(-4x^2 + 1x) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1|(-2sin(1\u03c0(-1|x - 2| + 3)) + 1) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(-2|(3sin(2\u03c0x + 3) + 2) + 2| + 2) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 5((1((-1x)/(3x - 2)) - 2)/(3((-1x)/(3x - 2)) - 1))^2 - 2((1((-1x)/(3x - 2)) - 2)/(3((-1x)/(3x - 2)) - 1)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-1(1(-2sin(3\u03c0x) - 2)^2 - 4(-2sin(3\u03c0x) - 2) - 5) + 3)/(-1(1(-2sin(3\u03c0x) - 2)^2 - 4(-2sin(3\u03c0x) - 2) - 5) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5(-4(4x^2 - 1x - 4)^2 + 3(4x^2 - 1x - 4) - 5)^2 - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5(-3(-1sin(2\u03c0x + 2) - 1) + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(-1|((1x + 2)/(-1x)) + 1| + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(3|(2x^2 - 3x + 3) - 2| + 2)^2 - 5(3|(2x^2 - 3x + 3) - 2| + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1sin(3\u03c0(-2|((1x - 2)/(2x))| - 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3|((3(4x^2 - 5x + 3) + 1)/(-2(4x^2 - 5x + 3))) + 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3cos(2\u03c0(1|(5x^2 + 5x - 4) - 1| - 3) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2((-1(4x^2 + 5x - 5) - 3)/(2(4x^2 + 5x - 5) + 1))^2 + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2cos(3\u03c0(1(-2x - 3)^2 + 1(-2x - 3) - 1) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(1(-1|x - 1| + 1)^2 - 4(-1|x - 1| + 1) + 1) - 1)/(1(1(-1|x - 1| + 1)^2 - 4(-1|x - 1| + 1) + 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3(-3(-3cos(2\u03c0x - 1) - 2)^2 + 5(-3cos(2\u03c0x - 1) - 2) - 1) - 2)/(1(-3(-3cos(2\u03c0x - 1) - 2)^2 + 5(-3cos(2\u03c0x - 1) - 2) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4((-3(-2sin(1\u03c0x + 3)) - 3)/(1(-2sin(1\u03c0x + 3))))^2 + 2((-3(-2sin(1\u03c0x + 3)) - 3)/(1(-2sin(1\u03c0x + 3)))) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2|(-3cos(1\u03c0(-3|x| - 3) + 2)) - 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3sin(1\u03c0(2|(-3|x - 3| - 3) + 2| + 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3((-1(-3|x + 1| + 3))/(-2(-3|x + 1| + 3) - 3))^2 - 3((-1(-3|x + 1| + 3))/(-2(-3|x + 1| + 3) - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(3cos(2\u03c0(-2x^2 - 1x + 4) - 3) - 1) - 3)/(2(3cos(2\u03c0(-2x^2 - 1x + 4) - 3) - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (3(2|(-2cos(3\u03c0x - 2) + 1) + 1| + 1) + 3)/(2(2|(-2cos(3\u03c0x - 2) + 1) + 1| + 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2|((3(1|x - 3|) + 3)/(-2(1|x - 3|) + 1)) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2(2(-2x^2 - 3x + 4)^2 - 4(-2x^2 - 3x + 4) + 1)^2 - 1(2(-2x^2 - 3x + 4)^2 - 4(-2x^2 - 3x + 4) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (3((3(-1sin(3\u03c0x - 2) - 2) + 3)/(1(-1sin(3\u03c0x - 2) - 2) - 3)) - 3)/(-1((3(-1sin(3\u03c0x - 2) - 2) + 3)/(1(-1sin(3\u03c0x - 2) - 2) - 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1(3sin(1\u03c0((1x - 1)/(3x - 1)) + 3) + 1)^2 - 3(3sin(1\u03c0((1x - 1)/(3x - 1)) + 3) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3e^(2(3|(3|x| + 3) + 3| - 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2e^(1(-2(2|x + 3| + 3)^2 - 3)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2|(-2(-1sin(1\u03c0x - 3) + 3) + 2) + 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (1(2e^(1(-2|x - 3|)) + 3) + 3)/(2(2e^(1(-2|x - 3|)) + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -5(-1sin(2\u03c0(-3|x + 1| - 1) - 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(3(-2e^(-2x) + 1)^2 - 1(-2e^(-2x) + 1) + 3) + 3)/(2(3(-2e^(-2x) + 1)^2 - 1(-2e^(-2x) + 1) + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3|(-4(-2e^(1x) + 1) - 5) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-2(3e^(2(1x^2 - 1x + 5)) + 2) + 2)/(-1(3e^(2(1x^2 - 1x + 5)) + 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(3cos(2\u03c0(-3x + 1) - 3) - 3)^2 + 1(3cos(2\u03c0(-3x + 1) - 3) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3e^(1(-1|((-2x + 2)/(-2x + 1)) + 3| + 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(4((3x - 2)/(-2x + 3)) + 1)^2 - 1(4((3x - 2)/(-2x + 3)) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-3e^(-2(-4x^2 + 3x))) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(-3(2x^2 + 4x - 3)^2 + 3(2x^2 + 4x - 3) + 5) + 2)/(-1(-3(2x^2 + 4x - 3)^2 + 3(2x^2 + 4x - 3) + 5) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2|(3sin(3\u03c0(4x + 5) - 1) + 1) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(-2e^(-2((1x + 1)/(-2x + 3))) + 2)^2 - 3(-2e^(-2((1x + 1)/(-2x + 3))) + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(1(-3sin(3\u03c0x + 1) - 1)^2 + 4(-3sin(3\u03c0x + 1) - 1) - 5) + 1| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3(-1sin(1\u03c0(-3x - 1) + 1) - 1)^2 - 5(-1sin(1\u03c0(-3x - 1) + 1) - 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2cos(3\u03c0(-5(1x^2 + 1x - 4) - 2) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(3cos(1\u03c0((-2x + 3)/(1x + 2)) - 1) + 1) - 3)/(3(3cos(1\u03c0((-2x + 3)/(1x + 2)) - 1) + 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(1cos(2\u03c0((3x - 2)/(1x)) - 3) - 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(1|(1sin(2\u03c0x + 3) + 2) - 3| + 2) - 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(2sin(1\u03c0(-1|x + 3|) + 3) - 2) + 1)/(-1(2sin(1\u03c0(-1|x + 3|) + 3) - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(2(2|x + 1| + 3)^2 - 1(2|x + 1| + 3) - 2)^2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 5(-3|(1x + 3) - 3| + 2)^2 - 4(-3|(1x + 3) - 3| + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3|(1|(-1cos(3\u03c0x - 3) - 3) + 2|) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2((-1(3|x - 1| + 2) + 3)/(2(3|x - 1| + 2) - 1))^2 + 2((-1(3|x - 1| + 2) + 3)/(2(3|x - 1| + 2) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(2(-4(-4x^2 + 4x - 3) - 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2sin(3\u03c0(-4((-1x - 3)/(2x + 2))^2 - 5((-1x - 3)/(2x + 2)) + 2) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (1(1sin(1\u03c0(-1x) - 3) + 3) + 1)/(-2(1sin(1\u03c0(-1x) - 3) + 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2sin(2\u03c0((3(1x^2 - 4) - 2)/(-3(1x^2 - 4) + 4)) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2e^(2((-2(-1x + 1) + 1)/(3(-1x + 1)))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(-4(3cos(2\u03c0x + 1) + 1)^2 + 5)^2 - 5(-4(3cos(2\u03c0x + 1) + 1)^2 + 5) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2sin(3\u03c0(4(4x - 4)^2 - 2(4x - 4) + 4) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1|(1|(-3x^2 + 2x - 1) + 1| - 1) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3sin(1\u03c0(5(1|x + 2| - 2) - 2) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1|((3x + 1)/(1x)) + 1|) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1cos(1\u03c0(-2(2|x + 2| + 2) + 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|((-3(-3x^2 - 5x) - 3)/(-1(-3x^2 - 5x) - 3)) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|(-2cos(2\u03c0(-3x^2 - 2x - 5) - 3) - 3) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1sin(2\u03c0(1(-2x^2 - 2x + 3)^2) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(3cos(3\u03c0(-2|x - 1|) + 3) + 1)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5((2(1cos(3\u03c0x) + 2) - 1)/(1(1cos(3\u03c0x) + 2)))^2 + 4((2(1cos(3\u03c0x) + 2) - 1)/(1(1cos(3\u03c0x) + 2))) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|(2sin(3\u03c0(1x^2 - 2x - 1) - 2) + 3) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2|((1(-2cos(3\u03c0x - 3)) + 1)/(-1(-2cos(3\u03c0x - 3))))| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1((-2(-5x^2 - 3x + 2) - 1)/(2(-5x^2 - 3x + 2) - 3)) - 3)/(-1((-2(-5x^2 - 3x + 2) - 1)/(2(-5x^2 - 3x + 2) - 3)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2cos(3\u03c0((-3(-4x^2 - 4x) + 1)/(-2(-4x^2 - 4x) - 1)) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(1e^(-1((3x + 3)/(2x + 2))) + 3)^2 - 1(1e^(-1((3x + 3)/(2x + 2))) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-4((2x + 3)/(1x + 3))^2 - 2)^2 + 1(-4((2x + 3)/(1x + 3))^2 - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-3((-1x - 2)/(1x + 3))^2 - 1((-1x - 2)/(1x + 3)) - 5)^2 + 5(-3((-1x - 2)/(1x + 3))^2 - 1((-1x - 2)/(1x + 3)) - 5) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-1(3cos(3\u03c0x + 1) - 1)^2 + 4(3cos(3\u03c0x + 1) - 1) - 5) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-3(-4x^2 + 5x + 3)^2 - 5(-4x^2 + 5x + 3) + 4) + 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(1(-2cos(1\u03c0x - 2) + 1) + 2)^2 + 1(1(-2cos(1\u03c0x - 2) + 1) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3|(-4(-3|x + 2|)^2 + 1(-3|x + 2|) + 4) + 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1(-1|(4x^2 - 5x - 4) - 2|) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(2|(4x + 1) - 2| - 2)^2 - 4(2|(4x + 1) - 2| - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1(2|(2sin(1\u03c0x + 2) + 2) + 2|) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3|(3(2sin(1\u03c0x - 1) - 2)^2 - 5(2sin(1\u03c0x - 1) - 2) + 2) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -5(-1sin(1\u03c0((2x - 1)/(-2x)) - 2) + 2)^2 + 5(-1sin(1\u03c0((2x - 1)/(-2x)) - 2) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-3e^(2(1x^2 - 1x + 2)) - 3) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3cos(1\u03c0(-5(-4x^2 - 5x + 1)^2 - 5(-4x^2 - 5x + 1)) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(2(3(-5x + 1)^2 - 4(-5x + 1))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (3(-2((-3x)/(-2x))^2 - 4((-3x)/(-2x)) + 5) - 1)/(2(-2((-3x)/(-2x))^2 - 4((-3x)/(-2x)) + 5) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(3(3sin(3\u03c0x) - 3) + 4) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3cos(3\u03c0(-5(-1|x - 1| + 1) - 2) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2|(2(-5x^2 - 3x)^2 - 1(-5x^2 - 3x) - 2)| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(-1(2e^(-1x) - 1)^2 + 3(2e^(-1x) - 1) + 1)^2 - 1(-1(2e^(-1x) - 1)^2 + 3(2e^(-1x) - 1) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(1sin(3\u03c0((-2x - 2)/(-3x - 2)) + 3) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(-2(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) + 1) - 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(2(2|x + 2| - 1)^2 - 4(2|x + 2| - 1)) - 2)/(2(2(2|x + 2| - 1)^2 - 4(2|x + 2| - 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(1(-3|x - 3|)^2 - 4(-3|x - 3|) - 1) + 1)/(-2(1(-3|x - 3|)^2 - 4(-3|x - 3|) - 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|(1|(-1cos(2\u03c0x - 1)) - 1|) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1sin(2\u03c0(2(-5x^2 + 3x)^2 + 1(-5x^2 + 3x) + 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3cos(2\u03c0(-3(1x + 4) - 2) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(-1cos(3\u03c0(5x^2 + 5x - 3)) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3sin(3\u03c0(1(2|x - 2|) + 4) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(-2(3sin(1\u03c0x - 1) + 2) + 1) - 1)/(-3(-2(3sin(1\u03c0x - 1) + 2) + 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(2|(1sin(2\u03c0x + 2) - 1)| - 2) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2cos(2\u03c0((2((-1x - 2)/(-2x - 3)) - 2)/(3((-1x - 2)/(-2x - 3)) + 3)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1|(-1|(2cos(2\u03c0x + 1)) + 1| + 2) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(-1e^(2((-2x)/(3x - 2))) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 5(-1|(3sin(2\u03c0x - 2) + 2) - 2|) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|(-4(-2x^2 + 4x + 4)^2 + 5(-2x^2 + 4x + 4)) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-1sin(3\u03c0((-1x - 3)/(-3x - 3)) + 1) - 2) - 3)/(1(-1sin(3\u03c0((-1x - 3)/(-3x - 3)) + 1) - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1(3(-1x^2 - 5x + 4)^2 - 2(-1x^2 - 5x + 4) + 1)^2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2(-1sin(1\u03c0(3x + 2) + 3) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(3e^(-2(2|x - 2| + 3)) + 1) - 1)/(1(3e^(-2(2|x - 2| + 3)) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1((-1(5x^2 - 2x + 2) + 2)/(-2(5x^2 - 2x + 2) + 3)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((-2(2|x - 3| + 1) - 2)/(-1(2|x - 3| + 1) + 3))^2 - 5((-2(2|x - 3| + 1) - 2)/(-1(2|x - 3| + 1) + 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3e^(-1(-2|(2|x| - 1) + 2| - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2(-1cos(1\u03c0(5x^2 - 3x + 1) - 3) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2|(-2(-3x^2 + 5x + 1)^2 - 5(-3x^2 + 5x + 1) - 4)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|((2(-4x^2 - 4) + 3)/(3(-4x^2 - 4) + 1))| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(1|(-3cos(3\u03c0x + 3) + 1) - 2| + 3) + 2)/(-3(1|(-3cos(3\u03c0x + 3) + 1) - 2| + 3) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-2(3sin(2\u03c0(-3|x - 1|) - 3) - 3) + 1)/(-2(3sin(2\u03c0(-3|x - 1|) - 3) - 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2e^(2((-1((-2x - 3)/(-2x - 2)) + 3)/(3((-2x - 3)/(-2x - 2)) - 2))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-4(2|x - 1|)^2 + 3(2|x - 1|) - 1)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(-1(1|x + 2| - 3)^2 - 4(1|x + 2| - 3) + 3) + 2)/(1(-1(1|x + 2| - 3)^2 - 4(1|x + 2| - 3) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2(-4(-2cos(1\u03c0x - 1) - 3) + 1)^2 + 1(-4(-2cos(1\u03c0x - 1) - 3) + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((1((-3x + 1)/(-1x + 2)) + 3)/(-1((-3x + 1)/(-1x + 2)) + 2))^2 + 4((1((-3x + 1)/(-1x + 2)) + 3)/(-1((-3x + 1)/(-1x + 2)) + 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(2cos(3\u03c0(-1|x - 3| + 2) + 1) + 1)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3((-1(-1x^2 + 5x - 4))/(3(-1x^2 + 5x - 4) - 1)) - 3)/(2((-1(-1x^2 + 5x - 4))/(3(-1x^2 + 5x - 4) - 1)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3sin(1\u03c0(3(-3|x - 2| - 1) + 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3(2cos(1\u03c0((-2x + 1)/(-2x + 3)) + 2))^2 - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2|(-4(2|x + 2| - 1)^2 + 5) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(2(-3cos(2\u03c0x - 3) + 1))^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3(-1cos(1\u03c0(-4x + 1) + 1) + 1)^2 + 1(-1cos(1\u03c0(-4x + 1) + 1) + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1e^(1(2|x + 1| - 1)) - 2)^2 - 1(-1e^(1(2|x + 1| - 1)) - 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-2(1x^2 - 5x) - 4) - 1)/(-3(-2(1x^2 - 5x) - 4) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(1(5x - 3)^2 + 3(5x - 3) + 1) - 3)/(-3(1(5x - 3)^2 + 3(5x - 3) + 1) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1(-3sin(3\u03c0(3|x - 2| - 2) + 3) - 1)^2 + 4(-3sin(3\u03c0(3|x - 2| - 2) + 3) - 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3(2cos(1\u03c0((2x + 3)/(-1x)) + 2) + 2)^2 + 4(2cos(1\u03c0((2x + 3)/(-1x)) + 2) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2sin(1\u03c0((-2(1x^2 - 5x - 1) - 2)/(-2(1x^2 - 5x - 1) + 1)) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5((-3((2x)/(-2x - 1)) - 2)/(-3((2x)/(-2x - 1)) - 3))^2 + 5((-3((2x)/(-2x - 1)) - 2)/(-3((2x)/(-2x - 1)) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-3(1|x + 3|)^2 - 1(1|x + 3|) + 2)^2 - 1(-3(1|x + 3|)^2 - 1(1|x + 3|) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2((-1(2cos(3\u03c0x + 1) + 1) - 2)/(2(2cos(3\u03c0x + 1) + 1) - 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(2sin(1\u03c0(-5x + 4) - 2) + 2) + 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4((-2(1x^2 + 5x - 4))/(-2(1x^2 + 5x - 4) - 2)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2cos(3\u03c0(1((3x + 2)/(-2x + 3)) + 2) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2e^(-1(-2((3x + 1)/(1x)) - 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -4(2sin(3\u03c0(-3|x - 2| - 1) - 1) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1cos(1\u03c0((3(1x^2 + 5x - 1) + 2)/(2(1x^2 + 5x - 1) + 1)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1cos(1\u03c0(2(-2x + 4)^2 - 3(-2x + 4) + 5) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(3\u03c0(-2|(-1|x| + 2) - 2| + 1) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|(-3cos(1\u03c0(-4x^2 - 5x + 5) - 2) + 3) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(2\u03c0(2(-4x^2 - 2x - 3) + 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1|(-1e^(2(5x + 5)) + 3) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|(-3(3|x + 3| + 3)^2 + 5(3|x + 3| + 3) - 3) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-2(-3(4x^2 + 1x - 1)^2 - 4(4x^2 + 1x - 1)) - 2)/(3(-3(4x^2 + 1x - 1)^2 - 4(4x^2 + 1x - 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|((1(1cos(3\u03c0x) + 1) + 3)/(-2(1cos(3\u03c0x) + 1))) - 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1(3|(-1|x| - 2) - 3| + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -5(-2sin(3\u03c0(-4x - 3)) - 1)^2 - 4(-2sin(3\u03c0(-4x - 3)) - 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1sin(2\u03c0(2|x - 1| + 2)) + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(4(1cos(3\u03c0x + 3) - 1)^2 + 3(1cos(3\u03c0x + 3) - 1) - 1) - 2)/(-1(4(1cos(3\u03c0x + 3) - 1)^2 + 3(1cos(3\u03c0x + 3) - 1) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3cos(1\u03c0((1(-4x) + 3)/(3(-4x) - 1)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(1sin(1\u03c0(3|x + 1| - 2) + 2) - 3) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-1e^(-2(-5x^2 - 4)) - 1)^2 + 1(-1e^(-2(-5x^2 - 4)) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3(1sin(3\u03c0((3x + 2)/(-2x + 1)) + 1) + 2)^2 + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3(2((3x + 1)/(2x - 1))^2 + 3) + 1)/(-1(2((3x + 1)/(2x - 1))^2 + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3|(4(-1x^2 + 5x - 5) + 5) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 3sin(2\u03c0(-2|(1x^2 - 3x + 4) + 2|) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(-3|((-2x + 2)/(2x)) + 1|)^2 + 3(-3|((-2x + 2)/(2x)) + 1|) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3e^(1(1|(4x - 5) - 3|)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(-5(2|x + 1| - 2)^2 - 4(2|x + 1| - 2) + 1) + 3)/(-1(-5(2|x + 1| - 2)^2 - 4(2|x + 1| - 2) + 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(1(-1|x - 2|)^2 - 5(-1|x - 2|) + 3)^2 - 2(1(-1|x - 2|)^2 - 5(-1|x - 2|) + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 5(1|(-3cos(1\u03c0x) - 2) + 3| + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2cos(3\u03c0(-4(5x + 4) - 5) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -4(5(5x^2 + 5x + 1)^2 - 1(5x^2 + 5x + 1) + 4)^2 - 4(5(5x^2 + 5x + 1)^2 - 1(5x^2 + 5x + 1) + 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 4(-3e^(1(2x^2 + 4x + 3)) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5((-2(-3|x + 1| + 3) + 1)/(-1(-3|x + 1| + 3) - 1))^2 - 1((-2(-3|x + 1| + 3) + 1)/(-1(-3|x + 1| + 3) - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3(-2sin(2\u03c0(-5x - 5) + 3) + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(1e^(1(3x^2 + 1x - 2)) + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (3(-1|(-2cos(1\u03c0x + 2) - 2) + 2| + 1) - 2)/(2(-1|(-2cos(1\u03c0x + 2) - 2) + 2| + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3cos(1\u03c0(2|(5x - 5) - 1| + 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2(1cos(1\u03c0(-4x - 4)) - 3)^2 - 5(1cos(1\u03c0(-4x - 4)) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3((-2(1sin(3\u03c0x) + 3) - 2)/(-1(1sin(3\u03c0x) + 3) - 3))^2 + 5((-2(1sin(3\u03c0x) + 3) - 2)/(-1(1sin(3\u03c0x) + 3) - 3)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-1(-2sin(1\u03c0x + 1) + 2)^2 - 4(-2sin(1\u03c0x + 1) + 2) - 2)^2 - 5(-1(-2sin(1\u03c0x + 1) + 2)^2 - 4(-2sin(1\u03c0x + 1) + 2) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2(-1sin(1\u03c0(-2x - 5) - 2) - 3) + 2)/(-2(-1sin(1\u03c0(-2x - 5) - 2) - 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3(-2(2sin(2\u03c0x + 1)) - 1)^2 - 2(-2(2sin(2\u03c0x + 1)) - 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(-4(3sin(1\u03c0x - 1) - 2) - 2) - 1)/(-1(-4(3sin(1\u03c0x - 1) - 2) - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(1cos(2\u03c0((2x - 1)/(-2x)) - 2) + 1))/(-1(1cos(2\u03c0((2x - 1)/(-2x)) - 2) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1|(5(2sin(3\u03c0x + 3) + 3) - 4) - 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(3((3x)/(-3x + 1)) - 5)^2 - 4(3((3x)/(-3x + 1)) - 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -5(-5(-2cos(2\u03c0x + 1) - 3) - 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -5(-1((-2x - 2)/(-3x - 2))^2 - 5((-2x - 2)/(-3x - 2)) - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(1(-1|x - 2| + 1)^2 - 1(-1|x - 2| + 1) - 3)^2 + 4(1(-1|x - 2| + 1)^2 - 1(-1|x - 2| + 1) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3|(2cos(1\u03c0(5x^2 + 5x - 2) - 3)) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(1\u03c0(-1|((-1x)/(-2x + 3)) - 3| + 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1(-1sin(1\u03c0((-1x - 3)/(2x - 1)) + 1) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 5((-1(-5x + 2) - 1)/(-3(-5x + 2) - 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1cos(2\u03c0(1|(-2|x - 1| - 1) - 1|) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3sin(2\u03c0(-4((-3x + 1)/(-1x - 2)) + 3) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(-2sin(1\u03c0((-2x - 2)/(-1x)) + 2)) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3sin(1\u03c0(3(3|x + 2| + 1) - 3) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2((-1(2|x + 1| + 1) + 2)/(1(2|x + 1| + 1)))^2 - 5((-1(2|x + 1| + 1) + 2)/(1(2|x + 1| + 1))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(-1((1(2x^2 - 5x - 2) + 2)/(2(2x^2 - 5x - 2)))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(2cos(3\u03c0(-1x + 5)) + 1)^2 - 1(2cos(3\u03c0(-1x + 5)) + 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(3|(-3sin(2\u03c0x - 1) + 2) + 3| - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(4(-2sin(3\u03c0x - 2))^2 - 4(-2sin(3\u03c0x - 2)) - 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((-1(2e^(-2x) - 1) + 1)/(-1(2e^(-2x) - 1) - 2))^2 + 1((-1(2e^(-2x) - 1) + 1)/(-1(2e^(-2x) - 1) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1e^(2(-1|((-2x)/(1x - 2)) + 1| - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1(2cos(3\u03c0((-2x + 1)/(1x + 1)) - 1))^2 + 2(2cos(3\u03c0((-2x + 1)/(1x + 1)) - 1)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1e^(2(-1((-3x + 3)/(-2x + 1)) - 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -4(2cos(2\u03c0(-1x^2 + 4x + 2) + 3) - 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(2|(3|x| + 1) + 2| - 3)^2 - 5(2|(3|x| + 1) + 2| - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2e^(-2((-3(-2x^2 - 4x + 2) + 3)/(1(-2x^2 - 4x + 2)))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-1(5(3sin(3\u03c0x + 2))^2 + 4(3sin(3\u03c0x + 2)) - 4) + 2)/(-3(5(3sin(3\u03c0x + 2))^2 + 4(3sin(3\u03c0x + 2)) - 4) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(2e^(-2(2|x + 1| - 1)) + 1) - 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-2(-4(-2cos(1\u03c0x - 1)) + 4) + 1)/(-1(-4(-2cos(1\u03c0x - 1)) + 4) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|(1|(-2|x| + 2) + 3| - 2) - 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(-2|(1cos(1\u03c0x - 2) + 2) + 1| + 2) - 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2e^(-1(-2|((2x)/(-1x + 3)) - 3| + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4((-3(-5x^2 + 4x - 1) - 3)/(3(-5x^2 + 4x - 1) + 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(-2sin(3\u03c0(2|x|) + 1) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2((-2(-2|x + 2| + 2))/(3(-2|x + 2| + 2) + 1))^2 - 4((-2(-2|x + 2| + 2))/(3(-2|x + 2| + 2) + 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3sin(1\u03c0((3(-5x))/(1(-5x) + 1)) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3(4(2sin(2\u03c0x + 3) - 3) - 4)^2 + 3(4(2sin(2\u03c0x + 3) - 3) - 4) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|(-2sin(3\u03c0(3x + 4) + 1) + 1)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3sin(3\u03c0(-2|(5x - 5)| - 3) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5(-1cos(3\u03c0(3x^2 + 2x - 3) - 3) - 3)^2 + 2(-1cos(3\u03c0(3x^2 + 2x - 3) - 3) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(2e^(1((2x + 2)/(-2x))) + 1)^2 - 4(2e^(1((2x + 2)/(-2x))) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-3(-2((-1x)/(-3x - 2))^2 - 4((-1x)/(-3x - 2)) + 4) - 2)/(-2(-2((-1x)/(-3x - 2))^2 - 4((-1x)/(-3x - 2)) + 4) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1sin(3\u03c0(-3|((-2x)/(-2x - 1)) + 1| - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(-1(2|x + 3| - 3)^2 + 3(2|x + 3| - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(-3|(2sin(3\u03c0x) - 1) + 2| - 2) + 1)/(-2(-3|(2sin(3\u03c0x) - 1) + 2| - 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2(2sin(2\u03c0(-5x - 2) + 2) + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-2(4(-1cos(1\u03c0x - 3) - 1) + 1) + 3)/(2(4(-1cos(1\u03c0x - 3) - 1) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1cos(2\u03c0(-1(1|x + 3| + 2) - 5) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4((2(3sin(2\u03c0x + 3) + 2) + 3)/(-3(3sin(2\u03c0x + 3) + 2) + 4))^2 + 3((2(3sin(2\u03c0x + 3) + 2) + 3)/(-3(3sin(2\u03c0x + 3) + 2) + 4)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-1(-3sin(1\u03c0x + 3) + 1)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2cos(2\u03c0(-1|(-1x^2 + 4x + 3) + 3|) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(2|(1sin(2\u03c0x - 3) + 1) + 2| - 3)^2 - 1(2|(1sin(2\u03c0x - 3) + 1) + 2| - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3e^(-1(2(-4x^2 - 4x + 3)^2 - 4(-4x^2 - 4x + 3) + 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1((-1(-3|x - 2|) - 2)/(-3(-3|x - 2|) - 1)) + 3)/(-1((-1(-3|x - 2|) - 2)/(-3(-3|x - 2|) - 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(-1(4x^2 - 5x - 3)^2 - 1(4x^2 - 5x - 3) - 3) - 3)/(-3(-1(4x^2 - 5x - 3)^2 - 1(4x^2 - 5x - 3) - 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|((2(4x^2 - 5x + 5) - 2)/(-2(4x^2 - 5x + 5) - 3)) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1((-2(-2x^2 + 4x - 1) - 1)/(-2(-2x^2 + 4x - 1) + 3))^2 + 2((-2(-2x^2 + 4x - 1) - 1)/(-2(-2x^2 + 4x - 1) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-1(-2cos(3\u03c0(1|x - 3| + 3) - 2) + 3) + 1)/(-1(-2cos(3\u03c0(1|x - 3| + 3) - 2) + 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(1|(2|x - 1| - 2)| + 2) - 2)/(-2(1|(2|x - 1| - 2)| + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -5(-4(3sin(3\u03c0x + 2)) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1|(1|(1sin(1\u03c0x) + 2) + 2| + 2) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(1(5(1x + 1)^2 + 2(1x + 1) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2|(1e^(2(-3x - 5)) - 1) - 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -5(3|(-1e^(1x) - 1) + 2| - 2)^2 - 2(3|(-1e^(1x) - 1) + 2| - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|((3(-2sin(1\u03c0x - 2) + 1) + 1)/(3(-2sin(1\u03c0x - 2) + 1) - 2)) - 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3(1sin(2\u03c0(-1|x + 2| - 1) + 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1cos(3\u03c0(-2|(-1x - 3) - 2| - 3) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 4(1cos(3\u03c0(-3x - 5)) + 2)^2 - 2(1cos(3\u03c0(-3x - 5)) + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1cos(3\u03c0(5(2|x|)^2 + 1(2|x|) + 4)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2(-4(-1cos(1\u03c0x + 2)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(1(1sin(1\u03c0x + 3) + 3) - 5) - 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(-3|(1x^2 + 1x - 1) + 1|)^2 + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(3|(-5x^2 + 1x - 4) - 2| - 1) + 3)/(3(3|(-5x^2 + 1x - 4) - 2| - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3e^(-1(3|(1|x + 2| - 2) - 1|)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(-1((3x + 3)/(2x - 1)) - 4)^2 - 4(-1((3x + 3)/(2x - 1)) - 4) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(-3|(3x^2 + 4x - 3) - 2| + 1)^2 - 2(-3|(3x^2 + 4x - 3) - 2| + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(-1|(-2|x| + 1)| - 1)^2 + 3(-1|(-2|x| + 1)| - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5(2(-1cos(3\u03c0x + 2) - 3)^2 - 2(-1cos(3\u03c0x + 2) - 3) + 4)^2 + 1(2(-1cos(3\u03c0x + 2) - 3)^2 - 2(-1cos(3\u03c0x + 2) - 3) + 4) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1|(2sin(3\u03c0(-4x - 3) + 2) + 3) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5((2(-1x^2 - 5x) + 1)/(1(-1x^2 - 5x))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2cos(1\u03c0((-2(-3x^2 + 3x - 4) - 2)/(-2(-3x^2 + 3x - 4) - 3)) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2|(-4(1x^2 - 5x - 1)^2 + 1(1x^2 - 5x - 1) - 1) - 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2|(5(-2|x + 1| + 1)^2 - 2(-2|x + 1| + 1) + 4) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1(2(-1x^2 - 3x + 3)^2 - 5(-1x^2 - 3x + 3))^2 - 3(2(-1x^2 - 3x + 3)^2 - 5(-1x^2 - 3x + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -5(1cos(2\u03c0(-2|x - 2| - 3) - 1) - 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1(-1sin(2\u03c0(-1x^2 - 2x - 1) + 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1(-2((-3x + 1)/(-2x - 3))^2 - 1((-3x + 1)/(-2x - 3)) - 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(2\u03c0(-2|((-2x - 3)/(3x + 1)) + 2| - 2) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(-3|((-1x - 1)/(1x + 3)) + 2| + 1)^2 + 1(-3|((-1x - 1)/(1x + 3)) + 2| + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3(1|(3x - 4) - 3| - 2)^2 + 5(1|(3x - 4) - 3| - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(3((2x)/(-2x + 1)) - 2) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-1(-1cos(2\u03c0(-5x + 4) - 3) - 1) + 1)/(-3(-1cos(2\u03c0(-5x + 4) - 3) - 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1cos(3\u03c0(1|(3|x + 2| + 2) - 2| - 3) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(1|(-4x^2 + 2) - 3| + 2)^2 + 4(1|(-4x^2 + 2) - 3| + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3sin(1\u03c0(1|(-3x) - 2| - 3) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3((2(-1|x - 3| + 2) + 3)/(-2(-1|x - 3| + 2) + 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-1|(-1|x + 3|) - 1| - 1)^2 + 5(-1|(-1|x + 3|) - 1| - 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3cos(2\u03c0(1((1x - 1)/(-1x + 2))^2 + 5((1x - 1)/(-1x + 2)) + 4) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1(-3(-1sin(2\u03c0x + 2) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(1(1sin(3\u03c0x + 2))^2 + 2(1sin(3\u03c0x + 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|(3(-1x^2 - 5x - 2) - 4) - 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-2(-2sin(3\u03c0((-1x + 1)/(2x + 1)) + 3) - 2) + 2)/(-1(-2sin(3\u03c0((-1x + 1)/(2x + 1)) + 3) - 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2(3cos(1\u03c0(-3x - 2)) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (2(3sin(2\u03c0((-1x + 3)/(-2x)) - 1) + 3) + 2)/(3(3sin(2\u03c0((-1x + 3)/(-2x)) - 1) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-1(-2cos(1\u03c0(-2x + 4) - 1) - 1) + 1)/(3(-2cos(1\u03c0(-2x + 4) - 1) - 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(-3|(-3x^2 + 2x - 2) + 2| - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3(3cos(1\u03c0(5x + 1) - 2) - 1)^2 + 4(3cos(1\u03c0(5x + 1) - 2) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (3(5(-2cos(2\u03c0x) - 1)^2 - 4(-2cos(2\u03c0x) - 1) + 4) + 3)/(1(5(-2cos(2\u03c0x) - 1)^2 - 4(-2cos(2\u03c0x) - 1) + 4) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(-4(2|x - 3| + 2)^2 - 3(2|x - 3| + 2) - 5)^2 - 2(-4(2|x - 3| + 2)^2 - 3(2|x - 3| + 2) - 5) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-3((-3(3x^2 + 4x + 2) - 3)/(-1(3x^2 + 4x + 2) - 1)) - 2)/(1((-3(3x^2 + 4x + 2) - 3)/(-1(3x^2 + 4x + 2) - 1)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3cos(1\u03c0((-1(4x - 1) + 1)/(1(4x - 1) + 1)) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3((-3(-4x^2 - 2x - 2) + 2)/(-1(-4x^2 - 2x - 2) - 2)) + 1)/(-1((-3(-4x^2 - 2x - 2) + 2)/(-1(-4x^2 - 2x - 2) - 2)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(3(5x^2 + 4x)^2 + 1(5x^2 + 4x) + 2) - 3)/(-1(3(5x^2 + 4x)^2 + 1(5x^2 + 4x) + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-2e^(1((1x - 1)/(1x))) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-1(-2|(-4x^2 + 1x - 2) + 3| + 1) - 2)/(3(-2|(-4x^2 + 1x - 2) + 3| + 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(1|(5x^2 - 4x + 1) - 2|)^2 + 1(1|(5x^2 - 4x + 1) - 2|) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3(-3sin(2\u03c0(4x^2 + 4x + 1) + 1) - 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3cos(1\u03c0((3((1x + 1)/(3x - 2)) - 2)/(1((1x + 1)/(3x - 2)) + 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(-1((-2x + 3)/(1x + 3))^2 - 2((-2x + 3)/(1x + 3)) + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -5(-1e^(1((2x + 3)/(2x - 3))) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|((-1(-3|x + 2| + 3) + 3)/(3(-3|x + 2| + 3) + 1)) - 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(-2((-2x - 2)/(3x))^2 - 1((-2x - 2)/(3x)) - 4) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2sin(1\u03c0(1((-3x - 2)/(-1x + 2)) - 1) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((-2(-3x - 3) + 1)/(-1(-3x - 3) + 3))^2 - 1((-2(-3x - 3) + 1)/(-1(-3x - 3) + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (3((-1(-2sin(3\u03c0x - 3) - 1) + 2)/(1(-2sin(3\u03c0x - 3) - 1) + 2)) + 1)/(2((-1(-2sin(3\u03c0x - 3) - 1) + 2)/(1(-2sin(3\u03c0x - 3) - 1) + 2)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3e^(-2(-3((-2x - 1)/(-2x - 2))^2 - 1((-2x - 1)/(-2x - 2)) + 4)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1(3((3x + 2)/(3x + 3))^2 - 2((3x + 2)/(3x + 3)) - 2)^2 + 1(3((3x + 2)/(3x + 3))^2 - 2((3x + 2)/(3x + 3)) - 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2((2(-2x^2 - 1x - 3) + 2)/(3(-2x^2 - 1x - 3) - 2))^2 + 2((2(-2x^2 - 1x - 3) + 2)/(3(-2x^2 - 1x - 3) - 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(-1sin(3\u03c0(4x + 2) - 3) + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(5(-3x^2 - 4x + 1)^2 - 1(-3x^2 - 4x + 1) - 4))/(-1(5(-3x^2 - 4x + 1)^2 - 1(-3x^2 - 4x + 1) - 4) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(3\u03c0((-1(-2x^2 - 1x + 3) - 1)/(3(-2x^2 - 1x + 3) + 1)) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2cos(1\u03c0(3|((3x)/(3x - 2)) + 2| + 1) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(2cos(2\u03c0(-2x^2 - 2x + 5) - 1) + 3)^2 + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2|(3sin(2\u03c0x - 3) - 3) + 2| - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3(3|(2sin(2\u03c0x + 3) - 3) - 1| - 3)^2 - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3e^(1((2(4x^2 + 2x + 4) - 2)/(3(4x^2 + 2x + 4) - 2))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1(5((2x - 1)/(-3x - 2)) + 4)^2 + 3(5((2x - 1)/(-3x - 2)) + 4) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1|(-5(-5x^2 + 4x + 1)^2 - 5(-5x^2 + 4x + 1) - 2)| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2sin(3\u03c0((1((-2x - 3)/(-3x + 1)) + 3)/(-3((-2x - 3)/(-3x + 1)) + 4)) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1e^(-2((-1(-1x^2 - 3x + 1) - 2)/(-2(-1x^2 - 3x + 1) + 3))) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(4(-3|x + 2| + 1)^2 + 3(-3|x + 2| + 1) - 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1cos(1\u03c0(-4(1x^2 + 1x + 1)^2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3e^(-1(5(-2|x + 1| + 2))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3e^(2((2(1|x + 2| - 2))/(3(1|x + 2| - 2) - 2))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2(3((3x - 2)/(-1x - 2))^2 - 3((3x - 2)/(-1x - 2)) + 5) - 1)/(-3(3((3x - 2)/(-1x - 2))^2 - 3((3x - 2)/(-1x - 2)) + 5) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3cos(2\u03c0((1(1|x - 3| - 1) - 1)/(-3(1|x - 3| - 1) + 4)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1(-2|(4x^2 + 3x - 3) + 3| - 3)^2 - 4(-2|(4x^2 + 3x - 3) + 3| - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(4(3cos(3\u03c0x) - 2) + 5) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|(1|(5x^2 + 3x) - 2| + 2)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2sin(1\u03c0(5(3|x + 2| - 2) - 4) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1sin(3\u03c0(1(-3x^2 + 5x - 1)^2 + 5(-3x^2 + 5x - 1) + 4) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(1(4x - 5)^2 + 5(4x - 5) - 5) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1e^(-1(-3|(-3x^2 + 1x) - 1|)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(2(4x^2 - 1x + 3)^2 - 4(4x^2 - 1x + 3) - 1) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(2|(-1|x - 3| + 3) - 2| - 3) + 3)/(-1(2|(-1|x - 3| + 3) - 2| - 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|(3(1x^2 + 5x - 5) - 3) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(1(-1x + 2)^2 + 3(-1x + 2) - 4) + 1)/(-2(1(-1x + 2)^2 + 3(-1x + 2) - 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(2sin(2\u03c0((3x - 3)/(-2x + 3)) + 1) + 1) - 2)/(1(2sin(2\u03c0((3x - 3)/(-2x + 3)) + 1) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1e^(1((-3(3|x + 2| - 1))/(-1(3|x + 2| - 1)))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3cos(1\u03c0(-2(2x - 3) + 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-2sin(3\u03c0(-2x^2 - 1x - 3) + 2) + 1) - 2)/(-2(-2sin(3\u03c0(-2x^2 - 1x - 3) + 2) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2((3((1x - 1)/(1x - 3)) + 2)/(1((1x - 1)/(1x - 3))))^2 + 5((3((1x - 1)/(1x - 3)) + 2)/(1((1x - 1)/(1x - 3)))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|((3(1x^2 - 5x + 1) - 1)/(-3(1x^2 - 5x + 1) + 2)) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2((2(-1x^2 - 5x - 4) + 3)/(-1(-1x^2 - 5x - 4) + 2)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((1(-4x^2 + 2x + 3) + 3)/(1(-4x^2 + 2x + 3)))^2 + 3((1(-4x^2 + 2x + 3) + 3)/(1(-4x^2 + 2x + 3))) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(3|((-1x + 2)/(3x))| + 1) + 1)/(-3(3|((-1x + 2)/(3x))| + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 5(3((3x + 3)/(-2x - 2)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-2(-1|(-1x - 3) + 3| - 3) + 1)/(-1(-1|(-1x - 3) + 3| - 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3sin(3\u03c0(-5(5x^2 - 2x - 3)^2 - 1(5x^2 - 2x - 3) - 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1cos(2\u03c0(1|(5x + 4) - 2| + 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(3|(1sin(2\u03c0x - 3) + 3) - 1| - 2) - 1)/(2(3|(1sin(2\u03c0x - 3) + 3) - 1| - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(2cos(1\u03c0(2x^2 + 4x + 2) - 2) - 3)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(-1((-3x + 2)/(-1x - 3)) + 4)^2 - 5(-1((-3x + 2)/(-1x - 3)) + 4) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1cos(1\u03c0(2|(-1x + 3) - 2| - 1) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(1\u03c0(1(1x^2 + 4x + 5) + 1) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3sin(3\u03c0(-1(-3|x + 1|) - 5) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -4(-2cos(3\u03c0((1x - 2)/(3x + 3)) - 3) + 1)^2 - 1(-2cos(3\u03c0((1x - 2)/(3x + 3)) - 3) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1(5(3|x| - 3)^2 + 3(3|x| - 3) - 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2cos(3\u03c0(2(-5x^2 - 5) + 5) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3((-1(3x^2 + 5x - 2) - 1)/(-2(3x^2 + 5x - 2))) - 2)/(-1((-1(3x^2 + 5x - 2) - 1)/(-2(3x^2 + 5x - 2))) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1|(-2e^(-1(-2|x + 3|)) + 2) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(2e^(-2(-5x^2 + 1x - 2)) - 1)^2 - 2(2e^(-2(-5x^2 + 1x - 2)) - 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2|(2cos(2\u03c0(5x^2 + 1x - 5) - 2) + 2) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (2(-1sin(1\u03c0(-3x + 3) + 2) - 1) + 2)/(2(-1sin(1\u03c0(-3x + 3) + 2) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (3(-2(-4x^2 - 4x + 1)^2 - 4(-4x^2 - 4x + 1) + 3))/(-2(-2(-4x^2 - 4x + 1)^2 - 4(-4x^2 - 4x + 1) + 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(1(-4x^2 - 2x - 5)^2 - 3(-4x^2 - 2x - 5) - 4) + 2)/(3(1(-4x^2 - 2x - 5)^2 - 3(-4x^2 - 2x - 5) - 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(2(2x - 3)^2 + 4(2x - 3) - 5) + 1)/(3(2(2x - 3)^2 + 4(2x - 3) - 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2(-2(-1x^2 + 3x - 4)^2 - 3(-1x^2 + 3x - 4) + 5)^2 + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1cos(2\u03c0(1|(4x^2 + 3x - 1) + 2| - 2) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2e^(-2(3|(4x - 4) + 2| + 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(-3(-2cos(1\u03c0x - 1) + 2) + 1)^2 - 3(-3(-2cos(1\u03c0x - 1) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|((1(2|x|) - 1)/(-1(2|x|) + 2)) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3e^(1(2(5x^2 + 4x) + 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3cos(3\u03c0((2(-4x + 3))/(-1(-4x + 3) + 3))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(3cos(1\u03c0(2|x| + 1) - 2))| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1cos(3\u03c0((-2((-1x - 2)/(2x - 1)) - 1)/(3((-1x - 2)/(2x - 1)) - 2)) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(3((-1x - 1)/(-3x + 4))^2 - 3((-1x - 1)/(-3x + 4)) - 3)| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -4(2|(-1x^2 - 2x - 4) + 2|)^2 - 5(2|(-1x^2 - 2x - 4) + 2|) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-1(4(-3x - 5)))/(-3(4(-3x - 5))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-3(-1x - 3)^2 + 4(-1x - 3) - 1))/(-2(-3(-1x - 3)^2 + 4(-1x - 3) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(1cos(1\u03c0((1x - 1)/(1x - 3)) - 3) + 2)^2 - 1(1cos(1\u03c0((1x - 1)/(1x - 3)) - 3) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-3|(5x^2 + 2x + 5) + 1| + 1) + 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3(5(-3cos(2\u03c0x + 2) - 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3sin(1\u03c0(-2(-1x^2 - 3x + 4) - 4) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|(-4(2sin(2\u03c0x + 3) + 2)^2 + 4(2sin(2\u03c0x + 3) + 2) - 4) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|(-2sin(1\u03c0(-5x^2 + 1x + 5) - 3) + 2)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2cos(3\u03c0(2(1|x - 2| - 2) - 1) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1sin(3\u03c0(1|(3|x + 2| - 2) - 1|) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2(-3cos(3\u03c0((1x + 3)/(3x)) + 3) + 2)^2 - 5(-3cos(3\u03c0((1x + 3)/(3x)) + 3) + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (3(-1|(3sin(3\u03c0x - 2)) + 3|) + 3)/(2(-1|(3sin(3\u03c0x - 2)) + 3|) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2sin(1\u03c0(-1(1x^2 + 2x - 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3((3(2|x|) - 2)/(-2(2|x|) - 1)) - 3)/(-1((3(2|x|) - 2)/(-2(2|x|) - 1)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-2(-4(2cos(3\u03c0x) + 1) + 4) + 1)/(-1(-4(2cos(3\u03c0x) + 1) + 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-2((-1(-3cos(1\u03c0x) - 1) - 2)/(-1(-3cos(1\u03c0x) - 1) + 2)) + 3)/(-1((-1(-3cos(1\u03c0x) - 1) - 2)/(-1(-3cos(1\u03c0x) - 1) + 2)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|((-1(-3sin(2\u03c0x + 1) - 3) + 1)/(-1(-3sin(2\u03c0x + 1) - 3) - 3))| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3|(-3(1x^2 - 2x - 1)) - 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1e^(-1((-2((-1x + 2)/(-3x + 2)) + 1)/(3((-1x + 2)/(-3x + 2)) + 1))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1|(-1cos(3\u03c0(2x + 5)) + 3) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(1cos(3\u03c0(5x^2 - 1x) - 3) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3sin(2\u03c0(2|(3x - 3) + 2| - 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (1(5(-2|x - 1|)^2 + 1(-2|x - 1|) - 3) + 3)/(-3(5(-2|x - 1|)^2 + 1(-2|x - 1|) - 3) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(2sin(3\u03c0(-2x^2 - 5x + 5) - 3) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2sin(2\u03c0((-1(-3x^2 + 3x))/(3(-3x^2 + 3x) + 2)) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(-1|((-1x)/(-3x + 2))| - 3) + 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2cos(3\u03c0(2|((-2x + 3)/(1x + 2)) + 1| + 3) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2cos(3\u03c0((2(1x) + 1)/(3(1x) - 2)) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1e^(1((3((3x - 3)/(1x - 3)) - 3)/(-1((3x - 3)/(1x - 3)) - 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3sin(2\u03c0((-2(-2x + 5))/(2(-2x + 5) - 1))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (3(-3sin(3\u03c0(-1x^2 + 2x - 2) + 2) + 2) - 3)/(-1(-3sin(3\u03c0(-1x^2 + 2x - 2) + 2) + 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2((-2(-1cos(1\u03c0x + 2) + 1) + 2)/(2(-1cos(1\u03c0x + 2) + 1) - 1)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3|((-3(3sin(2\u03c0x) - 2) + 1)/(-3(3sin(2\u03c0x) - 2) + 2)) - 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3|(-5((3x - 2)/(2x + 3))^2 - 1((3x - 2)/(2x + 3))) - 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1e^(-2((3(1x - 4))/(-3(1x - 4) + 1))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3|(-2cos(2\u03c0(-2x^2 + 5x) + 2) + 3) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-4(2|x| + 2)^2 - 2(2|x| + 2) + 5)| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3e^(1(-1(-1|x + 3| + 2) - 2)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2sin(1\u03c0(-2|((-3x - 1)/(-3x - 2)) - 3| + 3) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1((-1((-3x + 2)/(1x)))/(-1((-3x + 2)/(1x)) - 2))^2 + 1((-1((-3x + 2)/(1x)))/(-1((-3x + 2)/(1x)) - 2)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3sin(2\u03c0(-1(2x + 1)^2 + 4(2x + 1) + 2) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-2e^(2(-5x + 5)) + 3)^2 - 5(-2e^(2(-5x + 5)) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3e^(-1((3(-1x^2 + 4x + 1) + 1)/(2(-1x^2 + 4x + 1) + 2))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3(-1cos(2\u03c0(-5x^2 - 1x + 4) - 3) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(2|(-2cos(3\u03c0x) + 3) + 3| - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-1(2|(3cos(3\u03c0x) - 3) - 1| + 2) + 2)/(1(2|(3cos(3\u03c0x) - 3) - 1| + 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(5(-3cos(1\u03c0x - 3) - 1)^2 + 2)^2 + 3(5(-3cos(1\u03c0x - 3) - 1)^2 + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(3\u03c0(2(5x - 2)^2 + 5(5x - 2) + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2((3(1sin(3\u03c0x - 3) - 1) - 2)/(-1(1sin(3\u03c0x - 3) - 1) - 2)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|((1(-3|x + 2|) + 2)/(2(-3|x + 2|) + 1)) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2e^(1(-3|(2x + 3) - 1| - 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -5(3cos(2\u03c0(1x - 5) + 3))^2 - 2(3cos(2\u03c0(1x - 5) + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4((-3(-2e^(1x) + 1))/(-3(-2e^(1x) + 1) + 1))^2 - 3((-3(-2e^(1x) + 1))/(-3(-2e^(1x) + 1) + 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (3(3|(-1x^2 + 2x + 5) + 1| - 1) + 1)/(1(3|(-1x^2 + 2x + 5) + 1| - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1|(-1|((1x - 3)/(2x)) - 1| + 1) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(2cos(2\u03c0(3|x + 1| + 1) - 1) - 1))/(2(2cos(2\u03c0(3|x + 1| + 1) - 1) - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(2e^(2(2|x - 2| - 1)) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2((3(2sin(1\u03c0x - 2) + 1) + 2)/(3(2sin(1\u03c0x - 2) + 1) - 1)) + 2)/(3((3(2sin(1\u03c0x - 2) + 1) + 2)/(3(2sin(1\u03c0x - 2) + 1) - 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-2(1sin(3\u03c0x + 1)) - 1)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3|((-3(-1cos(1\u03c0x - 2) - 2) - 1)/(3(-1cos(1\u03c0x - 2) - 2) + 3)) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|(5(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) - 2) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (1(-2|(-1cos(2\u03c0x - 2) - 2) - 1| + 1) + 3)/(-1(-2|(-1cos(2\u03c0x - 2) - 2) - 1| + 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(1(3sin(1\u03c0x - 2) + 3)^2 - 2(3sin(1\u03c0x - 2) + 3) + 3) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-2((-3x - 2)/(3x))^2 - 2((-3x - 2)/(3x)) + 2)^2 - 3(-2((-3x - 2)/(3x))^2 - 2((-3x - 2)/(3x)) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2sin(2\u03c0((-2(2|x| - 2) - 3)/(3(2|x| - 2) - 2)) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(-3(-3sin(1\u03c0x - 3) + 2)^2 - 4(-3sin(1\u03c0x - 3) + 2) + 4) + 1)/(-3(-3(-3sin(1\u03c0x - 3) + 2)^2 - 4(-3sin(1\u03c0x - 3) + 2) + 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(-1|(-1x^2 - 3x + 1) - 3| - 2))/(-1(-1|(-1x^2 - 3x + 1) - 3| - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|(3sin(3\u03c0(4x + 5) - 2) - 1)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2(-1sin(1\u03c0(-3|x - 3| - 3) + 1) - 3)^2 + 3(-1sin(1\u03c0(-3|x - 3| - 3) + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1e^(-2((3(3|x + 3| - 1) - 2)/(3(3|x + 3| - 1) - 1))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3cos(3\u03c0(-3(-3|x| - 2) - 2) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (1(2sin(3\u03c0(-5x - 1) + 3)) + 1)/(2(2sin(3\u03c0(-5x - 1) + 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3(-3((3x - 1)/(1x))^2 + 3((3x - 1)/(1x)) + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|(1(-3e^(2x))^2 + 1(-3e^(2x)) - 1) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(2\u03c0(-1|((3x + 2)/(3x - 2)) - 2| + 3) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(-2(-4x^2) - 1) - 2)/(-3(-2(-4x^2) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-2|(5x - 1) + 2| + 3)^2 - 4(-2|(5x - 1) + 2| + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-5(-2cos(1\u03c0x - 3) - 2) - 1))/(3(-5(-2cos(1\u03c0x - 3) - 2) - 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2(3e^(1(-4x^2 + 5x + 2)) + 3)^2 - 1(3e^(1(-4x^2 + 5x + 2)) + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2((3(-1x - 4) - 2)/(1(-1x - 4) - 2))^2 - 2((3(-1x - 4) - 2)/(1(-1x - 4) - 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-1|((2x + 1)/(-2x)) + 1| - 2)^2 - 3(-1|((2x + 1)/(-2x)) + 1| - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5(-3|(-4x^2 - 4x - 4) - 3| + 2)^2 - 3(-3|(-4x^2 - 4x - 4) - 3| + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3sin(3\u03c0(4((3x)/(-3x - 1))^2 - 1((3x)/(-3x - 1)) + 4) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1|((1(-2sin(3\u03c0x + 3) + 2) - 3)/(-1(-2sin(3\u03c0x + 3) + 2) + 2)) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1cos(3\u03c0(3|(2|x + 3| - 1) + 1| + 2) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(2cos(2\u03c0(2x + 2) + 3) + 2)^2 - 3(2cos(2\u03c0(2x + 2) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-5(-3x^2 + 1x - 5)^2 + 5(-3x^2 + 1x - 5)) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(3((-3x)/(3x + 3))^2 - 2((-3x)/(3x + 3)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3|(1|(3x^2 + 4x + 4) + 2|) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2(3|(1cos(3\u03c0x - 2) - 1) - 1| - 2)^2 - 1(3|(1cos(3\u03c0x - 2) - 1) - 1| - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(-2|(1e^(-2x) + 1) + 3| - 2))/(-2(-2|(1e^(-2x) + 1) + 3| - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(3|(-3sin(3\u03c0x + 3) + 2) - 3| + 2)^2 + 4(3|(-3sin(3\u03c0x + 3) + 2) - 3| + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(-2|(-3sin(2\u03c0x + 2) - 2) + 3| - 2) + 2)/(-1(-2|(-3sin(2\u03c0x + 2) - 2) + 3| - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3sin(2\u03c0(-1(-5x^2 - 2x - 4) - 3) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -4(3|(-3cos(2\u03c0x + 3)) - 3|) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 5(-4(3sin(3\u03c0x + 2) + 2) - 2)^2 + 2(-4(3sin(3\u03c0x + 2) + 2) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(-4(1x^2 - 4x - 3)^2 + 4(1x^2 - 4x - 3) + 3) + 3)/(-3(-4(1x^2 - 4x - 3)^2 + 4(1x^2 - 4x - 3) + 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1((-3(-4x^2 + 3x))/(-1(-4x^2 + 3x) + 2))^2 + 1((-3(-4x^2 + 3x))/(-1(-4x^2 + 3x) + 2)) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4(-2|(-1sin(1\u03c0x - 2) + 1) - 1| + 3)^2 - 2(-2|(-1sin(1\u03c0x - 2) + 1) - 1| + 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(4(-3x^2 - 4x - 4)^2 - 5(-3x^2 - 4x - 4) - 4)| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3|(1|((2x)/(-1x + 2))| - 3)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 5((3(4x - 3) + 2)/(1(4x - 3) - 3))^2 - 2((3(4x - 3) + 2)/(1(4x - 3) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1sin(1\u03c0(-3((2x - 3)/(2x)) - 2) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-2(-2(1|x| + 2) + 5) - 2)/(1(-2(1|x| + 2) + 5) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3|(2(-2cos(2\u03c0x - 3)) - 3) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1((-2(-4x - 1) - 1)/(-1(-4x - 1) - 2))^2 - 5((-2(-4x - 1) - 1)/(-1(-4x - 1) - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1(-1(1sin(2\u03c0x + 2) - 3) + 5) + 3)/(-1(-1(1sin(2\u03c0x + 2) - 3) + 5) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3e^(2(-2(-1x - 1)^2 + 5(-1x - 1) + 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1sin(1\u03c0(1|(1x^2 - 1x - 1) + 2| + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1cos(1\u03c0((1(1x - 2) - 1)/(-1(1x - 2))) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 5(1sin(3\u03c0(-2x^2 + 2x + 1) - 3) - 3)^2 + 3(1sin(3\u03c0(-2x^2 + 2x + 1) - 3) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2e^(1(-1(-1|x + 3| - 3)^2 - 5(-1|x + 3| - 3) + 4)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2e^(-1(4(3|x + 1| + 3) + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(1e^(-1((1x - 1)/(3x))) - 3)^2 + 5(1e^(-1((1x - 1)/(3x))) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(-5((3x - 2)/(-2x + 3))^2 - 3((3x - 2)/(-2x + 3)) - 2) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|((1(5x^2 + 2x - 2) - 2)/(-3(5x^2 + 2x - 2) - 3)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1(-2e^(-2(-3|x - 3| - 2)) - 2)^2 - 4(-2e^(-2(-3|x - 3| - 2)) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-1(4(-1cos(3\u03c0x + 1) + 2)^2 - 2(-1cos(3\u03c0x + 1) + 2) + 2) + 1)/(3(4(-1cos(3\u03c0x + 1) + 2)^2 - 2(-1cos(3\u03c0x + 1) + 2) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1sin(3\u03c0(3(-2x + 3) - 4) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2sin(3\u03c0(-4(5x^2 - 5x - 5)) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(1((-3(-1|x| + 2) + 3)/(1(-1|x| + 2) + 2))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -5(-3|(-3cos(3\u03c0x)) + 3| + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (2(-1|(-3cos(2\u03c0x + 2) + 1) - 1| - 2) + 1)/(-3(-1|(-3cos(2\u03c0x + 2) + 1) - 1| - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(3(3|x| - 1) - 4)^2 + 3(3(3|x| - 1) - 4) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(-2(1|x|)^2 + 3(1|x|) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-1(2cos(2\u03c0((-2x + 2)/(-3x - 2)) + 1) + 2) + 2)/(-2(2cos(2\u03c0((-2x + 2)/(-3x - 2)) + 1) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3(-3((-2x - 3)/(-2x)))^2 + 1(-3((-2x - 3)/(-2x))) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(1((-2x + 3)/(1x + 2))^2 - 3((-2x + 3)/(1x + 2)))^2 - 5(1((-2x + 3)/(1x + 2))^2 - 3((-2x + 3)/(1x + 2))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5((-2(-1e^(2x) + 2) - 1)/(-2(-1e^(2x) + 2) + 3))^2 + 5((-2(-1e^(2x) + 2) - 1)/(-2(-1e^(2x) + 2) + 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3cos(3\u03c0(-3(3|x + 1| - 1)^2 + 2(3|x + 1| - 1) + 4) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(-2cos(1\u03c0(-1x - 2) - 2) + 3) - 1)/(-2(-2cos(1\u03c0(-1x - 2) - 2) + 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3cos(3\u03c0(-5((1x - 2)/(-3x))^2 - 4((1x - 2)/(-3x)) - 4) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2sin(3\u03c0((-1(4x - 4) + 3)/(-2(4x - 4) + 1)) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3(1|(-2cos(1\u03c0x - 3) - 1) + 3| + 3) + 3)/(1(1|(-2cos(1\u03c0x - 3) - 1) + 3| + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(1e^(-2(-2|x| + 1)) + 1)^2 + 1(1e^(-2(-2|x| + 1)) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1(-1sin(2\u03c0((-3x - 2)/(1x)) - 3) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2((2(3x^2 - 4x - 4) - 2)/(-2(3x^2 - 4x - 4) - 3)) + 3)/(-3((2(3x^2 - 4x - 4) - 2)/(-2(3x^2 - 4x - 4) - 3)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(-1cos(2\u03c0((-3x - 2)/(3x - 2)) - 1) - 3)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(3(2|x| + 3)^2 + 5(2|x| + 3) - 3) - 2)/(1(3(2|x| + 3)^2 + 5(2|x| + 3) - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(1|(-3|x + 2| - 1) + 3| + 3)^2 + 2(1|(-3|x + 2| - 1) + 3| + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(-1e^(1(-3|x + 3| + 2)) + 2) - 3)/(1(-1e^(1(-3|x + 3| + 2)) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(1(3cos(3\u03c0x + 1) + 3) + 5) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(-1|(-2|x - 1| + 3) - 1|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3|(-1cos(3\u03c0((-1x - 3)/(3x + 1)) + 1) + 3) + 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(1sin(1\u03c0(1x^2 + 1x + 4)) + 1) + 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(5(2x^2 + 1x - 5) + 2) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(-1e^(-1((-1x + 2)/(2x + 1))) + 1)^2 + 5(-1e^(-1((-1x + 2)/(2x + 1))) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(4(-2|x + 2| + 2) + 4) - 3)/(1(4(-2|x + 2| + 2) + 4) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5((-3((2x - 3)/(3x - 2)) + 1)/(2((2x - 3)/(3x - 2)) - 3))^2 + 5((-3((2x - 3)/(3x - 2)) + 1)/(2((2x - 3)/(3x - 2)) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-3|(1sin(2\u03c0x) - 3) + 3| + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1|((-2(2x^2 + 5x + 2) - 2)/(1(2x^2 + 5x + 2) + 2)) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(2(-3cos(1\u03c0x - 2) - 2)^2 - 2(-3cos(1\u03c0x - 2) - 2) - 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3(-3cos(2\u03c0(2x + 3) - 3) - 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3(3sin(3\u03c0(-2x^2 + 1x - 2) + 2) - 1)^2 + 2(3sin(3\u03c0(-2x^2 + 1x - 2) + 2) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2((2(-3cos(1\u03c0x) - 2) - 1)/(3(-3cos(1\u03c0x) - 2) - 2)) + 1)/(-3((2(-3cos(1\u03c0x) - 2) - 1)/(3(-3cos(1\u03c0x) - 2) - 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(2\u03c0(-1|(-3x^2 + 5x - 4) + 3| + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2e^(-1(5(3x^2 - 3x + 3))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (3(-5(-2cos(2\u03c0x) + 2) + 1))/(-2(-5(-2cos(2\u03c0x) + 2) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -5(3|(-4x^2 + 1x + 5) - 2| - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|((3(-2cos(3\u03c0x + 1) + 1) + 2)/(-1(-2cos(3\u03c0x + 1) + 1) - 2)) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (1(2sin(3\u03c0(4x - 2)) + 2) + 2)/(2(2sin(3\u03c0(4x - 2)) + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(3(3cos(3\u03c0x + 1) + 1) + 5) + 2)/(-3(3(3cos(3\u03c0x + 1) + 1) + 5) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(2(-5x + 4)^2 - 1(-5x + 4) + 1) - 3)/(1(2(-5x + 4)^2 - 1(-5x + 4) + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3((3(1x^2 + 3x - 3) + 1)/(1(1x^2 + 3x - 3))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(-1sin(3\u03c0((-2x + 3)/(2x + 1)) + 1) - 3)^2 + 5(-1sin(3\u03c0((-2x + 3)/(2x + 1)) + 1) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2cos(3\u03c0(3|(-5x + 5) + 1| + 3) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|(-2sin(3\u03c0(-2|x + 1| + 1) - 1) + 3) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-2(1(-2x - 3)^2 - 3(-2x - 3) + 5) + 2)/(-2(1(-2x - 3)^2 - 3(-2x - 3) + 5) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(-1|(-2e^(2x) + 3) - 2|) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1(1cos(3\u03c0((3x + 2)/(-2x - 1)) + 3) + 2)^2 - 2(1cos(3\u03c0((3x + 2)/(-2x - 1)) + 3) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 4(3|(-2sin(1\u03c0x - 2) + 1) - 2| - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3cos(2\u03c0(-1(-1x^2 - 4x) + 2) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2e^(1(2((1x - 2)/(3x))^2 + 3((1x - 2)/(3x)) - 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(3(-3x)^2 + 1(-3x) + 1) - 1)/(3(3(-3x)^2 + 1(-3x) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|(-3(1x^2 + 4x - 1) + 3) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1(2e^(-2(-4x^2 - 2x - 3)) + 3)^2 - 4(2e^(-2(-4x^2 - 2x - 3)) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|((2(3x^2 - 2x + 5))/(1(3x^2 - 2x + 5) + 2)) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-3(-1x^2 + 5x + 1) - 5) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(-2cos(1\u03c0(-4x + 3) + 2) + 1)^2 - 3(-2cos(1\u03c0(-4x + 3) + 2) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2e^(-2(-4(2|x + 1| + 1) - 5)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2((1((-2x - 2)/(2x + 1)) - 3)/(1((-2x - 2)/(2x + 1)) - 2))^2 + 1((1((-2x - 2)/(2x + 1)) - 3)/(1((-2x - 2)/(2x + 1)) - 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3cos(3\u03c0(-4(-1|x + 2| + 1) + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(-2((-2x)/(3x + 2)) + 4)^2 + 4(-2((-2x)/(3x + 2)) + 4) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3sin(2\u03c0(-3|(1x - 3) - 2|) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(2|(-2x^2 - 3x) + 1| + 2) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2((2(-1x^2 + 1x - 4) + 2)/(2(-1x^2 + 1x - 4))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3(3|(1|x + 1| - 1) + 1| + 1) + 3)/(-2(3|(1|x + 1| - 1) + 1| + 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1sin(1\u03c0(1(-3x) - 5) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(4((1x + 1)/(1x + 3)) + 2)^2 + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(3cos(3\u03c0(-2|x - 3| + 1) - 1) - 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(2e^(2(-3|x - 3| - 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2cos(1\u03c0((-2(-1x^2 + 5x + 3) - 3)/(1(-1x^2 + 5x + 3) + 3)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (2(-3(-3e^(2x) - 3)^2 + 1(-3e^(2x) - 3) - 5) - 2)/(2(-3(-3e^(2x) - 3)^2 + 1(-3e^(2x) - 3) - 5) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-3(-4(2sin(3\u03c0x - 2) - 3)^2 + 4(2sin(3\u03c0x - 2) - 3) + 5) - 3)/(-3(-4(2sin(3\u03c0x - 2) - 3)^2 + 4(2sin(3\u03c0x - 2) - 3) + 5)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2sin(3\u03c0(-3((1x + 2)/(-3x))) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2e^(-1(-1(2|x - 2| + 3)^2 + 3(2|x - 2| + 3) - 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1(4(-3|x - 3| + 3)^2 - 2(-3|x - 3| + 3))^2 - 4(4(-3|x - 3| + 3)^2 - 2(-3|x - 3| + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1|(-3(1cos(2\u03c0x) - 1)^2 - 2(1cos(2\u03c0x) - 1) - 5) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1cos(2\u03c0(-3(-3|x + 1| + 1)^2 + 2(-3|x + 1| + 1) - 2) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-3cos(2\u03c0(2|x - 3| + 1) - 2) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-2(5(3cos(1\u03c0x + 3) + 2)^2 + 5(3cos(1\u03c0x + 3) + 2) - 5) + 2)/(2(5(3cos(1\u03c0x + 3) + 2)^2 + 5(3cos(1\u03c0x + 3) + 2) - 5) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1sin(2\u03c0(5((1x - 1)/(2x + 1)) + 2) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3sin(2\u03c0(2|(1|x + 2| - 3) + 1| + 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3e^(-2(-2|(2x - 4) - 1| - 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2cos(1\u03c0(1(3x - 5)^2 + 2(3x - 5) - 4)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-2(-2(1sin(2\u03c0x) - 1) + 1) - 3)/(2(-2(1sin(2\u03c0x) - 1) + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(1(3x^2 + 3x + 5)^2 + 1(3x^2 + 3x + 5) + 1) - 1)/(-2(1(3x^2 + 3x + 5)^2 + 1(3x^2 + 3x + 5) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3cos(2\u03c0(2(4x^2 + 1x - 3) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}