{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3((2(-2x^2 + 4x + 5) - 1)/(1(-2x^2 + 4x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(-2(-3|(5x^2 - 1)| + 2) + 3) - 1)/(1(-2(-3|(5x^2 - 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 extremum with the largest y-value of the function f(x) = -3(3sin(3\u03c0x - 1))^2 + 4(3sin(3\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 rightmost local maximum of the function f(x) = -1((2(2|(2cos(3\u03c0x - 2) - 1) - 2| + 2) + 2)/(-2(2|(2cos(3\u03c0x - 2) - 1) - 2| + 2)))^2 + 1((2(2|(2cos(3\u03c0x - 2) - 1) - 2| + 2) + 2)/(-2(2|(2cos(3\u03c0x - 2) - 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": "How many local minima does the function f(x) = -1(-3|x + 3| + 3)^2 - 2(-3|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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2sin(3\u03c0(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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(2cos(3\u03c0((3x + 3)/(2x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(3cos(1\u03c0(1|x| - 1) - 3) - 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 local extremum of the function f(x) = -4(2|(4x^2 + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(3((2x - 1)/(3x)))^2 + 4(3((2x - 1)/(3x))) + 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) = -2((-2(-2|(4x^2 - 3x + 1) + 1| - 1) + 3)/(-2(-2|(4x^2 - 3x + 1) + 1| - 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 minimum of the function f(x) = (-1(-3|(-3e^(-2(1x^2 - 2x + 1)) - 3) - 3| + 2) - 1)/(-1(-3|(-3e^(-2(1x^2 - 2x + 1)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3sin(1\u03c0((1x - 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 average of all x-coordinates of local extrema of the function f(x) = -5((-2x + 1)/(-3x + 2))^2 + 3((-2x + 1)/(-3x + 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": "How many local minima does the function f(x) = -5((1(-1|(-5x^2 - 1x) - 1| - 3) - 3)/(-2(-1|(-5x^2 - 1x) - 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 rightmost local extremum of the function f(x) = -5(1cos(1\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(2cos(3\u03c0x - 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 extremum of the function f(x) = -2(-3e^(2x))^2 - 5(-3e^(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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(2x + 1)^2 + 3(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": "How many local maxima does the function f(x) = 5((-3x)/(2x + 2))^2 + 4((-3x)/(2x + 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 extremum of the function f(x) = -5((-3(-2(1|x + 2| - 3)^2 + 2(1|x + 2| - 3) + 5))/(2(-2(1|x + 2| - 3)^2 + 2(1|x + 2| - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-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 x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(-2|(2cos(1\u03c0(-3x^2 - 3x - 4)) + 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": "How many local minima does the function f(x) = -2(-2|(-2e^(1(1x^2 - 2x - 4)) - 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 rightmost local maximum of the function f(x) = -3(2sin(1\u03c0x + 2) + 2)^2 + 3(2sin(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 x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-1cos(1\u03c0x - 2) + 2) - 3)/(2(-1cos(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2(-1|(1sin(1\u03c0((-3x + 2)/(3x - 1)) + 1) + 3) + 1|)^2 - 3(-1|(1sin(1\u03c0((-3x + 2)/(3x - 1)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3|(-2cos(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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(1(-1((1x + 1)/(-1x + 3)) + 1)^2 + 5(-1((1x + 1)/(-1x + 3)) + 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 local minimum of the function f(x) = -1|(-2cos(2\u03c0((-3(-3x^2 - 4x - 5) + 1)/(3(-3x^2 - 4x - 5) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1((3(-4(-2|x - 3|)^2 - 2(-2|x - 3|)) - 1)/(2(-4(-2|x - 3|)^2 - 2(-2|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(5(3cos(3\u03c0(-1x - 4) - 3) - 2)^2 + 4))/(2(5(3cos(3\u03c0(-1x - 4) - 3) - 2)^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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1((-3(4(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 4) + 3)/(3(4(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 4))) - 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": "Find the x-coordinate of the local extremum of the function f(x) = (-3(5(-1|(-1x) - 2|)^2 - 4(-1|(-1x) - 2|) - 5) - 3)/(-2(5(-1|(-1x) - 2|)^2 - 4(-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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(3cos(2\u03c0(1x^2 - 1x + 2) + 3) - 2) + 2)/(-2(3cos(2\u03c0(1x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3((-1(1(2|x|) + 5) + 2)/(-2(1(2|x|) + 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 maximum with the smallest y-value of the function f(x) = 2|(5(1sin(2\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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(3(2|(-1sin(2\u03c0x + 1) + 3) - 2|) - 5)^2 + 3(3(2|(-1sin(2\u03c0x + 1) + 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3((-3x - 3)/(-2x - 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) = (2(1(-2|x + 1| - 1) + 4) + 1)/(-2(1(-2|x + 1| - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2((-1(4x^2 - 3x + 1) - 3)/(1(4x^2 - 3x + 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 minima does the function f(x) = -1(1|(3((-2x - 2)/(3x - 1)) - 5) - 1| + 2)^2 + 1(1|(3((-2x - 2)/(3x - 1)) - 5) - 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 minimum of the function f(x) = 1(3x + 2)^2 + 1(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(3(1e^(1(-1|x|)) - 3) + 1)^2 - 1(3(1e^(1(-1|x|)) - 3) + 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": "How many local minima does the function f(x) = 3e^(-2(1(4x^2 - 2x - 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 maximum of the function f(x) = 1|(-5(-2((1x - 1)/(-2x + 1))^2 - 4((1x - 1)/(-2x + 1)) + 4) + 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 local extremum with the largest y-value of the function f(x) = -3((1(2|(-1sin(2\u03c0x + 3) + 3) + 2| + 3) + 2)/(-2(2|(-1sin(2\u03c0x + 3) + 3) + 2| + 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": "How many local minima does the function f(x) = -4(-2|((-1(-1x - 2) - 2)/(2(-1x - 2) - 3)) - 1| - 1)^2 - 1(-2|((-1(-1x - 2) - 2)/(2(-1x - 2) - 3)) - 1| - 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) = -4((-1(-3x - 1) + 1)/(-2(-3x - 1) - 3))^2 - 4((-1(-3x - 1) + 1)/(-2(-3x - 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 minimum with the smallest y-value of the function f(x) = 4(-3sin(3\u03c0(1x - 4) - 3) + 3)^2 + 1(-3sin(3\u03c0(1x - 4) - 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 with the largest y-value of the function f(x) = -1(-2sin(1\u03c0(3|x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5(-3sin(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|((1x - 3)/(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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(3|((-1(2x) - 3)/(3(2x) - 2)) + 3|)^2 + 2(3|((-1(2x) - 3)/(3(2x) - 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 smallest y-value of the function f(x) = (3(-2cos(3\u03c0(-4(-2|x - 1|) + 5) - 2) + 3) + 1)/(2(-2cos(3\u03c0(-4(-2|x - 1|) + 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 of the function f(x) = -1(1e^(1(1|x| + 3)) + 1)^2 + 2(1e^(1(1|x| + 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 minimum with the largest y-value of the function f(x) = -2|(3cos(3\u03c0(-1x^2 - 1x) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(-1(-3(1e^(2x) + 2)^2 + 1(1e^(2x) + 2) + 2) + 2) + 1)/(-3(-1(-3(1e^(2x) + 2)^2 + 1(1e^(2x) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|((1(-2x^2 + 5x - 2) - 1)/(1(-2x^2 + 5x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((-1(-1(2|x|)^2 - 4(2|x|) + 4) - 2)/(2(-1(2|x|)^2 - 4(2|x|) + 4) + 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 average of all x-coordinates of local maxima of the function f(x) = (-1(-2|(2sin(2\u03c0x) + 2) - 1| + 3) - 1)/(-1(-2|(2sin(2\u03c0x) + 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 of the function f(x) = 5(-1x - 4)^2 - 5(-1x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-1cos(3\u03c0x - 1) + 2) + 3)/(1(-1cos(3\u03c0x - 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 rightmost local maximum of the function f(x) = -4((2(-3cos(3\u03c0x + 3) + 3))/(-2(-3cos(3\u03c0x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(1|(-2(5x^2 + 5x - 1) - 5) + 3| + 3) - 2)/(-2(1|(-2(5x^2 + 5x - 1) - 5) + 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 minimum of the function f(x) = 3((2(-4(1|x - 3| - 1) - 1))/(-3(-4(1|x - 3| - 1) - 1)))^2 - 5((2(-4(1|x - 3| - 1) - 1))/(-3(-4(1|x - 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 leftmost local extremum of the function f(x) = 1(-1cos(3\u03c0x - 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 rightmost local extremum of the function f(x) = (3(-1cos(3\u03c0(1(4x^2 - 5x + 2) - 4)) + 2) + 3)/(-1(-1cos(3\u03c0(1(4x^2 - 5x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3|(-4x^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(-1|x - 2| + 3)^2 + 4(-1|x - 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 average of all x-coordinates of local maxima of the function f(x) = -2(2sin(3\u03c0((-2x + 2)/(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 local maximum of the function f(x) = -1(4(-2|x - 3|) - 2)^2 - 4(4(-2|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3(-1|((-1(-5x^2 - 4x - 1) - 3)/(-3(-5x^2 - 4x - 1) + 4))| + 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(-2e^(-1(-1x^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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5((1(3(-1|x + 1| + 1)^2 + 2(-1|x + 1| + 1) - 4) - 3)/(2(3(-1|x + 1| + 1)^2 + 2(-1|x + 1| + 1) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1((-1(2x + 4) + 3)/(-2(2x + 4)))^2 - 1((-1(2x + 4) + 3)/(-2(2x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(-2e^(1((-1x - 3)/(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 with the largest y-value of the function f(x) = (-1(-2cos(1\u03c0x + 1) + 1) + 1)/(2(-2cos(1\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": "-8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-2|(-4(3cos(1\u03c0x + 1) - 1)^2 + 1(3cos(1\u03c0x + 1) - 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 minima of the function f(x) = -2((2(3sin(2\u03c0x + 1) + 3) - 1)/(-3(3sin(2\u03c0x + 1) + 3) + 1))^2 + 1((2(3sin(2\u03c0x + 1) + 3) - 1)/(-3(3sin(2\u03c0x + 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": "How many local minima does the function f(x) = -1|(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": "How many local maxima does the function f(x) = 1|((-2(-1(-4x^2 + 3x + 4) - 4) + 1)/(-3(-1(-4x^2 + 3x + 4) - 4) + 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 leftmost local extremum of the function f(x) = 4(1cos(1\u03c0x - 1) - 1)^2 - 2(1cos(1\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 extrema (both minima and maxima) does the function f(x) = -1|(5(3((3x + 1)/(3x + 2))^2 - 5((3x + 1)/(3x + 2)) - 3) + 5) + 3| - 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 leftmost local minimum of the function f(x) = 2cos(3\u03c0((1x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3(-1|(-3sin(1\u03c0x - 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 largest y-value of the function f(x) = 5(-1sin(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(2|x| + 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(2sin(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3sin(2\u03c0((1x + 2)/(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": "-3", "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(2|((-1(-5x^2 - 4x + 2))/(-2(-5x^2 - 4x + 2) - 1)) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2((1x + 1)/(-2x - 1))^2 - 1((1x + 1)/(-2x - 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 with the smallest y-value of the function f(x) = 5(-2cos(2\u03c0x - 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|(1(5x^2 + 2x - 3) + 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": "How many local minima does the function f(x) = -4(2x^2 - 3x - 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 with the largest y-value of the function f(x) = -3cos(2\u03c0(-1|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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-2(1cos(3\u03c0(2|x - 3| - 2) - 2) - 2)^2 - 4(1cos(3\u03c0(2|x - 3| - 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(-1(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 4) - 3)/(-1(-1(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-3|(2sin(2\u03c0(3x^2 - 3x - 3) - 2) + 2) + 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) = -1(-1(-1|x - 3| + 2)^2 - 3(-1|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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1sin(1\u03c0((-2(-4(-4x - 2)^2 - 4(-4x - 2) - 4) + 1)/(1(-4(-4x - 2)^2 - 4(-4x - 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 extremum of the function f(x) = -2(1(3e^(-1x) - 2) - 2)^2 + 4(1(3e^(-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": "Find the x-coordinate of the local extremum of the function f(x) = 1((-2x + 1)/(1x))^2 + 2((-2x + 1)/(1x)) - 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 extrema (both minima and maxima) does the function f(x) = -5(-1|(-1((2x - 3)/(2x + 3)) - 4) - 3| + 3)^2 - 1(-1|(-1((2x - 3)/(2x + 3)) - 4) - 3| + 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": "How many local extrema (both minima and maxima) does the function f(x) = -2|(1sin(2\u03c0(-1((2x + 1)/(-1x - 2))^2 + 5((2x + 1)/(-1x - 2)) - 5) + 3)) - 2| 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 rightmost local extremum of the function f(x) = -3|(-1((-3x + 1)/(-3x - 3))^2 + 5((-3x + 1)/(-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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-3(5(1cos(2\u03c0x + 2) - 3)^2 + 3(1cos(2\u03c0x + 2) - 3)) + 1)/(3(5(1cos(2\u03c0x + 2) - 3)^2 + 3(1cos(2\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 extremum of the function f(x) = (1(-5(-3(-2|x| - 2)^2 - 1(-2|x| - 2) - 4) + 1) - 1)/(1(-5(-3(-2|x| - 2)^2 - 1(-2|x| - 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": "How many local extrema (both minima and maxima) does the function f(x) = 1sin(2\u03c0((-2x + 2)/(-3x - 2)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(-1sin(2\u03c0(1((1x - 2)/(2x - 1))) - 2) - 3)^2 - 4(-1sin(2\u03c0(1((1x - 2)/(2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3e^(-1(-5x^2 + 5x - 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 smallest y-value of the function f(x) = 2|(2cos(3\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1|(1cos(3\u03c0x - 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 x-coordinate of the leftmost local minimum of the function f(x) = -2|(3(4((3x + 2)/(3x)) - 1)^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(-3(3((-1x + 3)/(-2x - 1)) - 4)^2 + 4(3((-1x + 3)/(-2x - 1)) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1e^(1(-4x)) + 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 average of all x-coordinates of local minima of the function f(x) = -3(-1cos(1\u03c0x + 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 average of all x-coordinates of local extrema of the function f(x) = 1e^(-1(1|(3(4x - 3)^2 + 2(4x - 3) + 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": "How many local extrema (both minima and maxima) does the function f(x) = 2sin(2\u03c0((1(-1(1|x - 2| - 1)^2 - 3(1|x - 2| - 1) - 1) - 3)/(1(-1(1|x - 2| - 1)^2 - 3(1|x - 2| - 1) - 1) + 1))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2|(-3((-2(3x^2 - 5x) - 1)/(-3(3x^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 extremum of the function f(x) = 3|(4(-3((2x + 2)/(-2x + 1)))^2 - 3(-3((2x + 2)/(-2x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(3((-1x + 1)/(-2x + 3)) + 2)^2 + 2(3((-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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(-2(-2sin(1\u03c0(-3|x + 1|) - 3) - 3) - 2) + 3)/(-1(-2(-2sin(1\u03c0(-3|x + 1|) - 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 x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(5(1|(2x + 5) - 2| - 2)^2 + 3(1|(2x + 5) - 2| - 2) + 1) + 1)/(-3(5(1|(2x + 5) - 2| - 2)^2 + 3(1|(2x + 5) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1x^2 - 4x - 1) + 3)/(-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 of the function f(x) = 3|((-1(4x^2 + 5x - 1) + 1)/(1(4x^2 + 5x - 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 extremum with the largest y-value of the function f(x) = 3cos(3\u03c0(-5x^2 - 5x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(-3|x + 3| + 2)^2 - 3(-3|x + 3| + 2) + 4 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 minimum with the smallest y-value of the function f(x) = 1sin(3\u03c0((-2(-1x^2 - 4x + 3) + 2)/(1(-1x^2 - 4x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2(-3sin(1\u03c0((1(-1x + 1) + 3)/(-3(-1x + 1) - 3)) - 3) + 2)^2 + 4(-3sin(1\u03c0((1(-1x + 1) + 3)/(-3(-1x + 1) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2(-3|((2(2x - 2) + 1)/(-3(2x - 2) - 3)) + 1| - 1)^2 - 3(-3|((2(2x - 2) + 1)/(-3(2x - 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|(-1(-1x - 5)^2 + 4(-1x - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(1|x| + 3)^2 - 5(1|x| + 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) = (1(-3cos(2\u03c0x + 1) - 2) - 2)/(1(-3cos(2\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1sin(2\u03c0(-4(-1|x + 1|) + 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 maximum of the function f(x) = -2sin(1\u03c0((1(5(-1x^2 - 3x - 5) - 5) + 1)/(1(5(-1x^2 - 3x - 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 average of all x-coordinates of local maxima of the function f(x) = -4(-2e^(2(2|x - 1| - 1)) + 1)^2 + 1(-2e^(2(2|x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1sin(1\u03c0(-1|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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1sin(3\u03c0(1|(-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 maximum of the function f(x) = -2e^(-2(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(5((-1(-1x + 4))/(2(-1x + 4) - 3))^2 - 3((-1(-1x + 4))/(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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(-3|(5(2e^(1x))^2 - 2(2e^(1x)) + 4) - 2|) + 2)/(-3(-3|(5(2e^(1x))^2 - 2(2e^(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 average of all x-coordinates of local minima of the function f(x) = -2cos(1\u03c0(3|x + 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3(-2((2(2|x - 1|) - 2)/(1(2|x - 1|) - 3))^2 - 1((2(2|x - 1|) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-2|x| + 1) - 2)/(-2(-2|x| + 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 average of all x-coordinates of local maxima of the function f(x) = -1cos(3\u03c0(-5((-2x - 3)/(-2x - 1))^2 + 2((-2x - 3)/(-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 local extremum with the largest y-value of the function f(x) = (-1(1sin(1\u03c0x + 2) - 1) - 3)/(2(1sin(1\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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5((1x - 1)/(2x + 1))^2 + 3((1x - 1)/(2x + 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 smallest y-value of the function f(x) = (-1(3(3|(-3sin(3\u03c0x - 2) + 3) - 2| - 1) - 4) + 1)/(3(3(3|(-3sin(3\u03c0x - 2) + 3) - 2| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1cos(2\u03c0((-1x)/(-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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2cos(2\u03c0(-1x^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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-2x^2 + 5x - 4) - 2)/(1(-2x^2 + 5x - 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": "How many local minima does the function f(x) = 4((-1(1(-1|x| - 3)^2) + 2)/(2(1(-1|x| - 3)^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 minimum of the function f(x) = 3(1|(4x - 1) + 1| + 3)^2 + 5(1|(4x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3(-2cos(3\u03c0(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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(2|(1(-5x^2 - 2x + 5) + 3)| - 2) + 3)/(1(2|(1(-5x^2 - 2x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3|(1cos(2\u03c0((1x + 2)/(-1x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3sin(3\u03c0(-1|x - 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": "How many local maxima does the function f(x) = (2(-1(-4x - 3)^2 + 1(-4x - 3) + 4) + 2)/(1(-1(-4x - 3)^2 + 1(-4x - 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 extremum of the function f(x) = -3sin(2\u03c0(-4x^2 + 5x + 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": "-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(-4x^2 - 4x + 3))/(3(-4x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((1(-1x + 3) - 1)/(2(-1x + 3) + 3))^2 + 3((1(-1x + 3) - 1)/(2(-1x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (3(1cos(2\u03c0x + 3) + 3) + 3)/(2(1cos(2\u03c0x + 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 minimum of the function f(x) = -3|(-3cos(2\u03c0x - 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 maxima does the function f(x) = 4(5x^2 - 1x - 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) = (-1(3|(-4(-5x^2 + 1x + 2) - 1) + 1| + 2) + 1)/(-3(3|(-4(-5x^2 + 1x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(2|(-3(5x^2 - 5x + 4) - 5) - 1| + 3) - 3)/(1(2|(-3(5x^2 - 5x + 4) - 5) - 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 of the function f(x) = (3(-5(2|(2e^(-1x) - 3) + 1|) - 2) + 1)/(-3(-5(2|(2e^(-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 of the function f(x) = 4(2|((1x + 2)/(3x - 2)) + 2| + 2)^2 - 5(2|((1x + 2)/(3x - 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": "0", "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(-1|(1x^2 + 2x) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1cos(3\u03c0(-3(-3((1x + 2)/(-3x - 2)) + 3)^2 - 5(-3((1x + 2)/(-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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(5x^2 + 3x) + 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 maximum with the smallest y-value of the function f(x) = 2(1|(-1cos(2\u03c0(-3x^2 - 4x - 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(1|(-2cos(1\u03c0x + 1))| - 2)^2 + 5(1|(-2cos(1\u03c0x + 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 x-coordinate of the local extremum of the function f(x) = 2|((-3x)/(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1sin(3\u03c0(-3x^2 + 4x - 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 minimum of the function f(x) = -1((2(3|(-2x + 1) + 2| - 2))/(3(3|(-2x + 1) + 2| - 2) - 2))^2 - 3((2(3|(-2x + 1) + 2| - 2))/(3(3|(-2x + 1) + 2| - 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 local extremum with the smallest y-value of the function f(x) = -1(-1cos(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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1e^(-2(2|(2(5x - 5)^2 - 2(5x - 5) - 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 extrema (both minima and maxima) does the function f(x) = -2((-1(1(3|x + 3| - 2)^2 - 4(3|x + 3| - 2) - 2) + 2)/(2(1(3|x + 3| - 2)^2 - 4(3|x + 3| - 2) - 2) - 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 average of all x-coordinates of local maxima of the function f(x) = -1|((2(1sin(2\u03c0x - 3) + 2) + 3)/(2(1sin(2\u03c0x - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1cos(3\u03c0((-1(-4x + 4) - 2)/(-3(-4x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(5((-1x + 1)/(-1x + 3))^2 - 2((-1x + 1)/(-1x + 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": "Find the average of all x-coordinates of local minima of the function f(x) = 5(-3(2sin(3\u03c0x - 3) - 3)^2 - 4(2sin(3\u03c0x - 3) - 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": "How many local minima does the function f(x) = -3|(2e^(1(2(-1x - 5)^2 + 4(-1x - 5) + 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 local minimum of the function f(x) = 1|(-2(1x^2 + 2x + 5) + 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) = 3e^(2(-5x - 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 minima of the function f(x) = -2|(1cos(3\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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1(-1(-2sin(1\u03c0(-2|x| - 3) + 1) - 2) + 1)^2 + 5(-1(-2sin(1\u03c0(-2|x| - 3) + 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 rightmost local maximum of the function f(x) = 4(-1(2|(-3sin(3\u03c0x) + 1) - 3| + 1) - 5)^2 + 4(-1(2|(-3sin(3\u03c0x) + 1) - 3| + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2cos(3\u03c0(1x^2 - 2x - 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 largest y-value of the function f(x) = 2(-2|(-2(-2cos(1\u03c0x + 2) + 1)^2 - 3(-2cos(1\u03c0x + 2) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(-4(2cos(2\u03c0x) + 3)^2 + 1(2cos(2\u03c0x) + 3) + 4) - 3)/(1(-4(2cos(2\u03c0x) + 3)^2 + 1(2cos(2\u03c0x) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(-4x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2e^(1(2((3x - 1)/(1x - 2))^2 - 2((3x - 1)/(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 average of all x-coordinates of local maxima of the function f(x) = -3|((-3(1cos(3\u03c0(2x^2 + 1x - 1) + 2) - 3) + 2)/(1(1cos(3\u03c0(2x^2 + 1x - 1) + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3|(-3sin(1\u03c0(-5((-2x + 3)/(-3x - 3))^2 - 3((-2x + 3)/(-3x - 3)) - 5) - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1|((1(1(-1x + 2)^2 + 1(-1x + 2) - 5) - 3)/(-2(1(-1x + 2)^2 + 1(-1x + 2) - 5) + 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) = (-2(-3|(-1(-4x - 4)^2 + 5(-4x - 4) + 2) - 2| + 3) - 2)/(-3(-3|(-1(-4x - 4)^2 + 5(-4x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(4(2|x - 3| + 1)^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 leftmost local maximum of the function f(x) = (-1(4(-3|(-3x^2 - 4x + 2)| - 2) + 4) + 3)/(1(4(-3|(-3x^2 - 4x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(1cos(2\u03c0x + 3) + 1))/(-2(1cos(2\u03c0x + 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 of the function f(x) = (3(-2(-3|x - 1| + 2) + 4) + 3)/(-3(-2(-3|x - 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": "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((1(-1x - 3) - 3)/(1(-1x - 3) + 1))^2 + 2((1(-1x - 3) - 3)/(1(-1x - 3) + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1sin(1\u03c0(2(-3x^2 - 4x - 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) = (-1(-2x^2 - 2x + 3) + 2)/(-3(-2x^2 - 2x + 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 maxima of the function f(x) = 3(4(1sin(2\u03c0(-1|x - 1| - 3) + 1))^2 + 1(1sin(2\u03c0(-1|x - 1| - 3) + 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) = (3(1x^2 + 3x + 1))/(1(1x^2 + 3x + 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 extremum of the function f(x) = -3|(-2sin(1\u03c0x - 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 leftmost local extremum of the function f(x) = 4(-2sin(2\u03c0(1|x + 1| + 3) + 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 minimum with the smallest y-value of the function f(x) = 5(2cos(3\u03c0x) - 3)^2 + 4(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-1x^2 - 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 extrema (both minima and maxima) does the function f(x) = -3|(-1cos(3\u03c0(5(4x^2 - 2x - 1) + 4) - 1) + 2) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(-1(-3|x + 3| + 1)^2 + 4(-3|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 minimum of the function f(x) = 3cos(1\u03c0(-5x^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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-2(2sin(2\u03c0((3x + 1)/(-3x - 3)) - 3) + 2) - 1)^2 - 5(-2(2sin(2\u03c0((3x + 1)/(-3x - 3)) - 3) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5((-1(-2|(4x^2 + 3x) + 2| - 3) + 2)/(3(-2|(4x^2 + 3x) + 2| - 3) - 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 average of all x-coordinates of local extrema of the function f(x) = 1|(3cos(3\u03c0x + 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 rightmost local extremum of the function f(x) = 3((3(-2sin(2\u03c0x + 3) + 1) - 1)/(-3(-2sin(2\u03c0x + 3) + 1) - 3))^2 + 4((3(-2sin(2\u03c0x + 3) + 1) - 1)/(-3(-2sin(2\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3(-1|(-5x^2 - 2x - 5) + 2| - 3))/(-2(-1|(-5x^2 - 2x - 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": "How many local extrema (both minima and maxima) does the function f(x) = (-3(-2e^(-1(-3x^2 + 2x + 4)) + 2) + 3)/(3(-2e^(-1(-3x^2 + 2x + 4)) + 2) - 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 average of all x-coordinates of local extrema of the function f(x) = (3(1cos(1\u03c0x - 2) + 1) + 3)/(1(1cos(1\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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(-2|x| + 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": "How many local maxima does the function f(x) = -1(-3((3x + 3)/(1x + 3))^2 - 3((3x + 3)/(1x + 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 rightmost local minimum of the function f(x) = 2(-2|(-1cos(2\u03c0x + 2) + 3) - 3| - 1)^2 + 5(-2|(-1cos(2\u03c0x + 2) + 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": "10", "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 - 3| - 3)^2 + 3(2|x - 3| - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(1e^(1((1(-3x + 4) - 1)/(-2(-3x + 4) + 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 maximum with the smallest y-value of the function f(x) = 4(3(-1sin(3\u03c0(2|x - 2| + 1) - 2) - 1)^2 - 5(-1sin(3\u03c0(2|x - 2| + 1) - 2) - 1) - 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 extremum of the function f(x) = 1e^(1(-1|((2x + 2)/(-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) = -1(-3((-3(1sin(3\u03c0x + 2) + 2) + 3)/(-3(1sin(3\u03c0x + 2) + 2) - 3)) - 3)^2 - 4(-3((-3(1sin(3\u03c0x + 2) + 2) + 3)/(-3(1sin(3\u03c0x + 2) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1|(-3(1((-2x + 1)/(1x + 2)) - 3)^2 - 4(1((-2x + 1)/(1x + 2)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(1(1x^2 + 5x + 3) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(2|(-4x^2 + 4x - 3) - 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 minima of the function f(x) = -1|(-1x^2 - 5x) - 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 leftmost local extremum of the function f(x) = (1(1cos(1\u03c0x + 3) + 2) - 2)/(-3(1cos(1\u03c0x + 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 minima does the function f(x) = 2|(-4x^2 - 4x + 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 rightmost local extremum of the function f(x) = (1(4(-1|x + 1| + 3)^2 - 1(-1|x + 1| + 3) - 2) - 2)/(3(4(-1|x + 1| + 3)^2 - 1(-1|x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2((2(1e^(-1x) - 3) - 1)/(3(1e^(-1x) - 3) - 1))^2 - 3((2(1e^(-1x) - 3) - 1)/(3(1e^(-1x) - 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 leftmost local extremum of the function f(x) = 4(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-3sin(2\u03c0(-2x - 3) + 1)) + 3)/(2(-3sin(2\u03c0(-2x - 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 leftmost local minimum of the function f(x) = (3(-2(2(-3|x - 3| + 3) - 3)^2 - 2(2(-3|x - 3| + 3) - 3) + 3) - 3)/(-3(-2(2(-3|x - 3| + 3) - 3)^2 - 2(2(-3|x - 3| + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2cos(1\u03c0(-3|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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(-1e^(2(2|x + 3| + 3)) - 1) + 3)/(2(-1e^(2(2|x + 3| + 3)) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1|(-1x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (1(4(3|x| + 1)^2 + 1(3|x| + 1) + 2) - 1)/(-1(4(3|x| + 1)^2 + 1(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 maxima does the function f(x) = 2e^(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 average of all x-coordinates of local extrema of the function f(x) = -3|(-1(5(-1cos(3\u03c0x - 1) + 1)^2 - 4(-1cos(3\u03c0x - 1) + 1) + 2) - 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": "How many local minima does the function f(x) = -3((-2(-1x - 3) + 1)/(3(-1x - 3) + 2))^2 + 4((-2(-1x - 3) + 1)/(3(-1x - 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 extremum of the function f(x) = (2(4(-2|x + 3| + 1) - 2) + 2)/(-2(4(-2|x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(-1sin(2\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2((-2(-3|(2cos(3\u03c0x - 3) + 2) + 2| - 2) + 3)/(2(-3|(2cos(3\u03c0x - 3) + 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": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-1(-3(-1cos(1\u03c0x + 1) - 1)^2 - 4(-1cos(1\u03c0x + 1) - 1) - 4) + 1)/(2(-3(-1cos(1\u03c0x + 1) - 1)^2 - 4(-1cos(1\u03c0x + 1) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(1((-2(-2x^2 - 4x + 1) + 2)/(-2(-2x^2 - 4x + 1) - 3)) + 5) + 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(2|(5(-5x^2 + 2x - 2)) - 3|) - 2)/(3(2|(5(-5x^2 + 2x - 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 leftmost local extremum of the function f(x) = 1|(1(-3((2x + 2)/(-3x - 1)) - 1)^2 + 4(-3((2x + 2)/(-3x - 1)) - 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 leftmost local minimum of the function f(x) = 1((-3(-1(1|x + 2|) + 5) - 2)/(-1(-1(1|x + 2|) + 5) + 2))^2 + 2((-3(-1(1|x + 2|) + 5) - 2)/(-1(-1(1|x + 2|) + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2sin(3\u03c0(1|x + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3|(-4x^2 + 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": "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((1x + 3)/(-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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-1|((1(-3x^2 - 2) - 3)/(-2(-3x^2 - 2) + 3)) - 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 rightmost local minimum of the function f(x) = -2sin(3\u03c0(4((-3x - 2)/(3x - 2))^2 + 4((-3x - 2)/(3x - 2)) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3|(-2e^(1(-2x^2 + 2x - 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 extremum with the largest y-value of the function f(x) = (-2(-2|(-1(2sin(3\u03c0x - 1) - 2)^2 + 4(2sin(3\u03c0x - 1) - 2))| - 1) + 1)/(2(-2|(-1(2sin(3\u03c0x - 1) - 2)^2 + 4(2sin(3\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 local maximum with the largest y-value of the function f(x) = 2|(-2cos(2\u03c0x + 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1e^(1((-3(-1|(3x^2 + 5x - 1)| - 3) + 3)/(2(-1|(3x^2 + 5x - 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 minimum of the function f(x) = 1(4(2|x + 3| + 1) + 2)^2 + 3(4(2|x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (1(-1cos(2\u03c0x) - 1))/(-1(-1cos(2\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 extremum of the function f(x) = -2((1x - 3)/(1x))^2 - 5((1x - 3)/(1x)) - 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) = (2(-2|(-2(-2x - 2)^2) + 1| - 2) + 1)/(2(-2|(-2(-2x - 2)^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 local extremum with the smallest y-value of the function f(x) = 2sin(2\u03c0(-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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(-5(2|(3sin(2\u03c0x - 1) + 1) + 3| + 2) - 1) + 1)/(2(-5(2|(3sin(2\u03c0x - 1) + 1) + 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) = -2cos(2\u03c0(1(1x + 5)^2 + 3(1x + 5) - 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 x-coordinate of the local extremum with the largest y-value of the function f(x) = -1((1(-2|(-1x^2 - 4x - 4) + 3| - 2) + 1)/(1(-2|(-1x^2 - 4x - 4) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3((3x + 2)/(-2x - 2))^2 - 1((3x + 2)/(-2x - 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 smallest y-value of the function f(x) = -1cos(2\u03c0(4x + 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 maximum of the function f(x) = (-1(-3cos(2\u03c0(-3(-4x^2 + 1x + 5) + 2)) + 3) + 2)/(1(-3cos(2\u03c0(-3(-4x^2 + 1x + 5) + 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 minimum with the smallest y-value of the function f(x) = -3(1|(1sin(1\u03c0x - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2sin(3\u03c0(1|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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|(1e^(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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|((-2x)/(-2x + 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 maximum of the function f(x) = -2|(-3sin(3\u03c0((-1(1x^2 - 3x) + 1)/(3(1x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(-1x^2 - 1x + 4) + 1)/(-3(-1x^2 - 1x + 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 rightmost local extremum of the function f(x) = 3e^(1((2(2|(1x^2 - 4x + 5) - 3| - 1))/(1(2|(1x^2 - 4x + 5) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(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 average of all x-coordinates of local minima of the function f(x) = -1|(5x^2 + 1x) - 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) = -3sin(2\u03c0((1x - 2)/(-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 of the function f(x) = 2e^(-1((2(-5(-3|x| + 1) + 4) + 1)/(-1(-5(-3|x| + 1) + 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": "How many local extrema (both minima and maxima) does the function f(x) = 1sin(2\u03c0((2(-1(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 5) - 1)/(3(-1(2|x + 2| - 3)^2 - 5(2|x + 2| - 3) + 5) + 1)) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(3|x - 3| - 3)^2 + 4(3|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": "Find the average of all x-coordinates of local minima of the function f(x) = 2cos(2\u03c0(-1|x - 2| - 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 rightmost local minimum of the function f(x) = 3((1x - 1)/(-2x + 3))^2 + 4((1x - 1)/(-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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3((-1x - 2)/(-1x + 2))^2 + 2((-1x - 2)/(-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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-2|((-1(-5x^2 + 5x - 1) - 3)/(2(-5x^2 + 5x - 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": "How many local maxima does the function f(x) = 3|(-3x^2 + 3x - 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 rightmost local minimum of the function f(x) = -1cos(1\u03c0(-5((3(-5x^2 + 4x - 4) - 2)/(-1(-5x^2 + 4x - 4) + 2)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-2cos(3\u03c0(-1(-1|x + 3| + 1) + 5) - 3) - 2)^2 + 2(-2cos(3\u03c0(-1(-1|x + 3| + 1) + 5) - 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 x-coordinate of the local extremum of the function f(x) = 5(-4((3x - 1)/(2x))^2 + 2((3x - 1)/(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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(3x^2 - 1x - 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 local maximum with the smallest y-value of the function f(x) = 2(2|(-3sin(1\u03c0(4x + 3) + 3) - 1)| - 3)^2 + 4(2|(-3sin(1\u03c0(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": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(1\u03c0(-3(-4x + 4)^2 + 3(-4x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(5x^2 - 3x + 4) + 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) = (3(-5x^2 + 3x + 1) - 3)/(-3(-5x^2 + 3x + 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) = 3sin(1\u03c0(-4x^2 - 5x + 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 minimum of the function f(x) = -4(-5x^2 + 4x - 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 largest y-value of the function f(x) = (1(-2(2cos(3\u03c0x + 2) - 1)^2 - 5(2cos(3\u03c0x + 2) - 1) + 1) - 3)/(-2(-2(2cos(3\u03c0x + 2) - 1)^2 - 5(2cos(3\u03c0x + 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) = (1(2x^2 + 2x - 2) - 1)/(3(2x^2 + 2x - 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 leftmost local maximum of the function f(x) = 2|(-1cos(2\u03c0((-1x - 2)/(-1x + 2)) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 5(3|((-1(-1x^2 - 2x - 5) + 3)/(-1(-1x^2 - 2x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(-3|x| + 1) - 3)/(1(-3|x| + 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|(-2((-2(-3x^2 + 5x + 3))/(-1(-3x^2 + 5x + 3) + 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 local maximum with the smallest y-value of the function f(x) = 3sin(3\u03c0(1x^2 - 3x) + 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) = 1((-2(-3x^2 - 1x - 1) + 3)/(1(-3x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 3cos(3\u03c0(-1x^2 + 5x - 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) = 3sin(3\u03c0((-1x + 1)/(3x - 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 of the function f(x) = -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 leftmost local minimum of the function f(x) = -1(1cos(1\u03c0x + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5(3e^(-1x) - 3)^2 - 4(3e^(-1x) - 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 rightmost local extremum of the function f(x) = 1|(2(-4(-2sin(2\u03c0x + 2) + 2) - 3)^2 + 5(-4(-2sin(2\u03c0x + 2) + 2) - 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": "How many local maxima does the function f(x) = -1((-1(5x^2 + 2x + 4) + 1)/(1(5x^2 + 2x + 4))) + 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 maximum of the function f(x) = -3(-5(2sin(1\u03c0((2x - 3)/(1x)) + 2) + 1) - 4)^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": "How many local maxima does the function f(x) = -1|(3cos(1\u03c0((-2x)/(2x + 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 x-coordinate of the leftmost local minimum of the function f(x) = -3|((2(-2(1x^2 + 2x - 4) + 1) - 3)/(2(-2(1x^2 + 2x - 4) + 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 rightmost local extremum of the function f(x) = -3|((-2(-1(1x^2 + 3x - 5) + 3) + 3)/(-3(-1(1x^2 + 3x - 5) + 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 with the largest y-value of the function f(x) = 1e^(1(-2|(-5(1x + 4)^2 + 1(1x + 4) - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|(-1(-4x + 4)^2 + 2(-4x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(2|(-2x - 4) - 1| + 3)^2 + 1(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 maximum with the smallest y-value of the function f(x) = -2sin(3\u03c0(3(3((1x - 3)/(-2x + 1)) + 3)^2 + 5(3((1x - 3)/(-2x + 1)) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3cos(2\u03c0((-2x - 1)/(3x + 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 maxima of the function f(x) = 3(-3sin(3\u03c0(5((1x + 2)/(-3x + 2))^2 - 3((1x + 2)/(-3x + 2)) + 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) = 1sin(2\u03c0(2|(5x + 5) - 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": "How many local maxima does the function f(x) = 1(-2|(1((-3x - 2)/(-1x - 3))^2 + 1((-3x - 2)/(-1x - 3)) - 3) + 3| + 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 minimum with the largest y-value of the function f(x) = (1(3sin(2\u03c0x - 3) - 3) + 1)/(-2(3sin(2\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3((-2(-2sin(1\u03c0(5x^2 - 2x - 4) + 2) + 1) + 2)/(-2(-2sin(1\u03c0(5x^2 - 2x - 4) + 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 rightmost local minimum of the function f(x) = 2sin(1\u03c0((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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1cos(1\u03c0(-1(5((-1x + 3)/(-3x + 1))^2 - 1((-1x + 3)/(-3x + 1)) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3e^(-1((-3x - 1)/(-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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3(2|((1x + 1)/(-2x)) + 3| + 1)^2 - 1(2|((1x + 1)/(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(2|(4(-1x^2 + 1x) + 5) - 2| - 3) + 3)/(-1(2|(4(-1x^2 + 1x) + 5) - 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 local extremum with the largest y-value of the function f(x) = -1|(1sin(2\u03c0x + 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(-1sin(3\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(4(2(3|x| - 3) - 1)^2 - 1(2(3|x| - 3) - 1) - 4))/(-2(4(2(3|x| - 3) - 1)^2 - 1(2(3|x| - 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": "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(3e^(-1(2x^2 - 1x - 2)) - 1) - 1)/(-2(3e^(-1(2x^2 - 1x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-5x^2 - 5x + 5) + 3)/(3(-5x^2 - 5x + 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 leftmost local minimum of the function f(x) = 4(3|((-1x - 1)/(-3x - 2)) + 1| - 3)^2 + 1(3|((-1x - 1)/(-3x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5((2x + 3)/(1x + 1))^2 + 2((2x + 3)/(1x + 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 minimum of the function f(x) = 4(-5x)^2 - 4(-5x) - 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": "How many local maxima does the function f(x) = 5(2|(-2((2x)/(2x - 1)) - 4) + 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 local extremum of the function f(x) = -5(-3|(2x^2 + 3x + 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 rightmost local extremum of the function f(x) = 2e^(2(-3|(-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": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-1x - 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 extrema (both minima and maxima) does the function f(x) = -2|(-2cos(2\u03c0x) + 1) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(1\u03c0(2x^2 - 2) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -5(-2|(-3x^2 + 4x - 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 maxima does the function f(x) = -2(-2|((3(-4x^2 + 4x - 5) + 1)/(-2(-4x^2 + 4x - 5) + 3)) - 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 minimum of the function f(x) = -3(2cos(1\u03c0(-3|x - 3| + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1sin(1\u03c0(-1|(-4x^2 - 3x - 2) - 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": "How many local minima does the function f(x) = -3(-1e^(2((1x - 1)/(1x - 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 x-coordinate of the local maximum with the largest y-value of the function f(x) = -3cos(2\u03c0(4x + 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) = 1(-1|x - 2|)^2 + 5(-1|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 local maximum of the function f(x) = -3|(1e^(-2(-1x^2 - 2x + 5)) + 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": "6", "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(3|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": "-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(-4(-3|x + 2| + 2)^2 + 4(-3|x + 2| + 2) - 5) + 3) - 1)/(2(-3(-4(-3|x + 2| + 2)^2 + 4(-3|x + 2| + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1sin(2\u03c0(2(2|x + 2| - 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -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 local extremum with the smallest y-value of the function f(x) = -3sin(1\u03c0(-2(1|((3x + 3)/(3x + 1)) - 2| - 2) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|(2((-1(1x - 3) - 1)/(2(1x - 3) + 1))^2 - 4((-1(1x - 3) - 1)/(2(1x - 3) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(2(-1e^(2(4x^2 - 4x - 3)) - 3) + 2))/(-3(2(-1e^(2(4x^2 - 4x - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|(2sin(1\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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(1(-4x^2 - 1x + 1) - 4))/(-1(1(-4x^2 - 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": "How many local maxima does the function f(x) = 3|(-1e^(2(5((-3x - 1)/(-1x))^2 - 4((-3x - 1)/(-1x)) - 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 local maximum with the smallest y-value of the function f(x) = -1sin(3\u03c0((-1x - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(-1(4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) - 5) + 2))/(-1(-1(4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) - 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 maximum of the function f(x) = 2e^(-1(5(2|((-2x - 2)/(-2x)) + 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) = 2((-2(1|(1sin(2\u03c0x + 2) + 2) - 1| - 1) - 2)/(2(1|(1sin(2\u03c0x + 2) + 2) - 1| - 1) - 3))^2 - 2((-2(1|(1sin(2\u03c0x + 2) + 2) - 1| - 1) - 2)/(2(1|(1sin(2\u03c0x + 2) + 2) - 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 minima does the function f(x) = -5((-2x - 1)/(-1x + 2))^2 - 3((-2x - 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 minimum of the function f(x) = 1((-2x - 3)/(-1x))^2 + 1((-2x - 3)/(-1x)) + 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(3|(1e^(-1x) + 2) - 2| - 1)^2 + 4(3|(1e^(-1x) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3sin(1\u03c0(-1|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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2(1sin(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2sin(1\u03c0(-1|(-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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(5((1(1|x - 3| - 1) + 3)/(2(1|x - 3| - 1) - 1)) - 2)^2 + 4(5((1(1|x - 3| - 1) + 3)/(2(1|x - 3| - 1) - 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 maxima of the function f(x) = 1|((-2(-2(5x + 3)^2 - 3(5x + 3) + 5) - 1)/(-2(-2(5x + 3)^2 - 3(5x + 3) + 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": "-1", "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(1\u03c0(4x^2 + 5x + 3)) - 1) + 5) - 3)/(2(-2(3cos(1\u03c0(4x^2 + 5x + 3)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-1|((2x + 2)/(-3x))| - 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 of the function f(x) = (-1(3(4x)^2 - 4) - 3)/(-3(3(4x)^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": "0", "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((-2x)/(3x - 1)) - 1) + 3)^2 - 4(-2sin(2\u03c0((-2x)/(3x - 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": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1|((-3(-1cos(1\u03c0x + 3)) - 2)/(-3(-1cos(1\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3sin(2\u03c0(-5(-3|x - 3| + 3)^2 + 2(-3|x - 3| + 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 average of all x-coordinates of local extrema of the function f(x) = 3|(-3sin(3\u03c0x - 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": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3sin(3\u03c0(-2(5x + 3)^2 + 5(5x + 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": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3sin(1\u03c0(2|x - 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) = -3(3(1e^(-1x) - 2)^2 - 3(1e^(-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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-3(-3|(1x - 2) - 2| + 3) + 3)/(-1(-3|(1x - 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 x-coordinate of the local maximum of the function f(x) = -2(1((2x + 2)/(-1x + 3))^2 - 2((2x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-2(-2|(2(1x^2 + 4x + 1) + 2) - 2| + 3) - 3)/(3(-2|(2(1x^2 + 4x + 1) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(2sin(1\u03c0((1x - 2)/(2x - 1)) - 1) + 2)^2 - 5(2sin(1\u03c0((1x - 2)/(2x - 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 average of all x-coordinates of local maxima of the function f(x) = 5(-3((3(2|x + 1| + 1))/(-1(2|x + 1| + 1))) + 4)^2 + 5(-3((3(2|x + 1| + 1))/(-1(2|x + 1| + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3sin(3\u03c0(1x^2 - 4x - 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) = 1|(5(-1x^2 + 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 extremum of the function f(x) = 1cos(1\u03c0((-3(-3|(2x - 1) - 1| - 2) + 3)/(-2(-3|(2x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(1|(4x) - 2| - 2)^2 + 3(1|(4x) - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(1(-5((2x + 1)/(-2x + 3))^2 + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(5x^2 + 4x - 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 maximum with the largest y-value of the function f(x) = (-3(2e^(-1x) - 1))/(1(2e^(-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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|(-2sin(1\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 leftmost local minimum of the function f(x) = 2|(1((-3(1x - 3) + 2)/(-2(1x - 3)))^2 - 1((-3(1x - 3) + 2)/(-2(1x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(-2|(4x^2 - 5x + 5) + 1| + 2) - 2)/(1(-2|(4x^2 - 5x + 5) + 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 maximum of the function f(x) = -1(1|(2sin(2\u03c0((2x + 2)/(3x)) + 3) - 2) - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1e^(-1(3x^2 - 5x + 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 smallest y-value of the function f(x) = 1e^(2(4((-3(3|x - 3| - 1))/(-2(3|x - 3| - 1) + 3))^2 + 5((-3(3|x - 3| - 1))/(-2(3|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1e^(-2(2|(-2((-3x - 2)/(1x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2cos(1\u03c0(-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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(3\u03c0(1((-1x + 2)/(2x - 1))^2 - 4((-1x + 2)/(2x - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2cos(3\u03c0(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3(3sin(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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(3sin(3\u03c0x - 3) - 2)^2 - 1(3sin(3\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 minima of the function f(x) = (-3(-1(-1|(1cos(1\u03c0x + 3) + 2) - 3| - 1)) + 1)/(-3(-1(-1|(1cos(1\u03c0x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|(2(2(3cos(1\u03c0x + 3) - 1)^2 - 2(3cos(1\u03c0x + 3) - 1) + 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": "Find the x-coordinate of the local extremum of the function f(x) = (-2(-4x^2 - 2x + 2) - 1)/(1(-4x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(1(4(1|x + 1| - 2)^2 - 4(1|x + 1| - 2) + 4) + 1) + 1)/(1(1(4(1|x + 1| - 2)^2 - 4(1|x + 1| - 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": "How many local maxima does the function f(x) = -1|(-3(1x^2 - 4x) + 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 local maximum with the largest y-value of the function f(x) = (2(3cos(3\u03c0x - 2) - 1) - 1)/(-2(3cos(3\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": "Find the x-coordinate of the local minimum of the function f(x) = 3e^(-2(2|(5x) + 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 extremum with the smallest y-value of the function f(x) = 2(1|x - 3| - 1)^2 - 1(1|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-5(4x + 4)^2 - 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 maximum of the function f(x) = 2cos(2\u03c0(2|x + 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) = -2cos(1\u03c0(2(1|(2x + 2) + 3| + 2)^2 - 3(1|(2x + 2) + 3| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -5(-4(-1e^(-2(1|x - 3| + 1)))^2 - 2(-1e^(-2(1|x - 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": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3cos(2\u03c0(-3(-2|x| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2e^(-2(-1|((-1x + 1)/(2x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2e^(2(3((-3x)/(-2x + 3))^2 - 5((-3x)/(-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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-2x + 5)^2 + 4(-2x + 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 of the function f(x) = 2e^(-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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3(-3sin(1\u03c0x) + 1) - 3)/(-3(-3sin(1\u03c0x) + 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) = -2cos(3\u03c0(-2x^2 - 1x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-3|(-5x^2 + 4x - 1) - 2| - 3) - 2)/(3(-3|(-5x^2 + 4x - 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": "How many local minima does the function f(x) = -3(-4((-2x + 2)/(-3x + 1)) - 2)^2 + 1(-4((-2x + 2)/(-3x + 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 leftmost local maximum of the function f(x) = 3cos(3\u03c0(-1x^2 - 5x - 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 with the smallest y-value of the function f(x) = -3sin(2\u03c0(1|x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4(-1cos(3\u03c0x) + 3)^2 - 2(-1cos(3\u03c0x) + 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 minimum of the function f(x) = 3e^(1(-5(-1((2x + 1)/(-1x - 2))^2 + 5((2x + 1)/(-1x - 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 local minimum of the function f(x) = 3(2x^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 leftmost local maximum of the function f(x) = -1((3(3(2|x| - 2)^2 - 2(2|x| - 2) + 4) + 3)/(2(3(2|x| - 2)^2 - 2(2|x| - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3(-3|(-1(1e^(1x) - 3) + 5) - 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 leftmost local minimum of the function f(x) = 3cos(3\u03c0(-3(-2|x - 3| + 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": "How many local minima does the function f(x) = (-1(-1cos(3\u03c0x) - 3))/(1(-1cos(3\u03c0x) - 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 extremum of the function f(x) = -2(3x - 5)^2 - 3(3x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(3|(5(5x^2 + 5x - 5) + 4)| - 3))/(2(3|(5(5x^2 + 5x - 5) + 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 smallest y-value of the function f(x) = 4(-2cos(3\u03c0x + 3) - 1)^2 - 4(-2cos(3\u03c0x + 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) = 4(-3sin(3\u03c0((-1(3|x - 1| + 1) - 3)/(2(3|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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2|(2cos(3\u03c0((-1(-5x^2 + 2x - 1) - 2)/(-3(-5x^2 + 2x - 1) - 1)) + 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 local extremum with the largest y-value of the function f(x) = 2sin(2\u03c0(4(3|x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|((-3x - 1)/(1x)) + 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 extrema of the function f(x) = 3(-3cos(2\u03c0(-1((-3x - 2)/(2x))^2 - 5((-3x - 2)/(2x)) + 5) + 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": "How many local extrema (both minima and maxima) does the function f(x) = -3sin(1\u03c0(1(-3x^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": "565", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3(3|(-3sin(2\u03c0(1x + 2) + 1) + 1) - 2|) - 3)/(-1(3|(-3sin(2\u03c0(1x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((-3(1|(5x + 1) - 2| + 1) + 3)/(-2(1|(5x + 1) - 2| + 1) - 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 maximum with the largest y-value of the function f(x) = 4(1cos(2\u03c0(-2(-2|x + 1| - 1) - 5) + 2) + 3)^2 - 3(1cos(2\u03c0(-2(-2|x + 1| - 1) - 5) + 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": "How many local maxima does the function f(x) = (-3(2(1x^2 + 4) + 4) - 1)/(3(2(1x^2 + 4) + 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) = (2(3cos(1\u03c0x + 1) - 2) - 1)/(3(3cos(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": "-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|((2x + 1)/(2x + 3)) - 2| + 3)^2 - 5(-2|((2x + 1)/(2x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4(-5x^2 + 5x - 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": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1(-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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-2|(3x^2 - 1x) + 1| + 1) - 3)/(2(-2|(3x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(-1|(3cos(2\u03c0x - 3) - 2) - 2| - 1)^2 + 2(-1|(3cos(2\u03c0x - 3) - 2) - 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 average of all x-coordinates of local maxima of the function f(x) = (3(-2(3|(-1sin(1\u03c0x - 3) - 1) + 1| - 2) - 1) + 2)/(-2(-2(3|(-1sin(1\u03c0x - 3) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1cos(1\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 extremum of the function f(x) = (-1(4(2x^2 + 2x + 4) + 4))/(1(4(2x^2 + 2x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|((2(-3(-5x^2 - 4x - 1) - 2) + 1)/(1(-3(-5x^2 - 4x - 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 local maximum with the smallest y-value of the function f(x) = -3sin(3\u03c0(-3|((1(3x^2 - 1x) - 3)/(1(3x^2 - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3e^(2(-3x^2 - 4x)) + 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) = 1cos(3\u03c0(-5(3x - 5)^2 + 5(3x - 5) - 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 maxima of the function f(x) = (-3(2(2(-2|x - 1|)^2 + 4(-2|x - 1|) + 3) + 1))/(1(2(2(-2|x - 1|)^2 + 4(-2|x - 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 leftmost local minimum of the function f(x) = -4((-1(-3sin(2\u03c0x + 3) - 1) - 3)/(-3(-3sin(2\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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(1|x| + 3)^2 + 1(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(4x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2(-3|(-3x - 3) - 3| + 1)^2 + 3(-3|(-3x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(3((1(2|x + 2| - 3) + 2)/(-2(2|x + 2| - 3) - 1)) - 4)^2 + 2(3((1(2|x + 2| - 3) + 2)/(-2(2|x + 2| - 3) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2cos(1\u03c0(-3|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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2cos(1\u03c0(2|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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|((1(2(1x + 1)^2 + 1(1x + 1) - 5) - 2)/(3(2(1x + 1)^2 + 1(1x + 1) - 5) + 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 average of all x-coordinates of local minima of the function f(x) = -3(2(1cos(1\u03c0x + 3) - 3)^2 + 2(1cos(1\u03c0x + 3) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3|(-4(1((2x - 1)/(1x + 1))^2 + 4((2x - 1)/(1x + 1)) - 4) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(-2|x + 2| + 1) - 2)/(-2(-2|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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3e^(-2(2(-2((3x - 1)/(3x + 2))^2 + 3((3x - 1)/(3x + 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 minimum of the function f(x) = 1(-3x + 1)^2 + 3(-3x + 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 extrema of the function f(x) = (1(1(-2sin(3\u03c0(1|x + 2| + 3) - 3)) - 3) + 3)/(1(1(-2sin(3\u03c0(1|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": "0", "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\u03c0x + 3))^2 + 2(1cos(1\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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2(-5(1|(-3cos(3\u03c0x + 2)) - 1| - 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 maximum of the function f(x) = -3|(-1((-1(2x^2 + 5) + 2)/(2(2x^2 + 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1e^(1(-1((-1x - 2)/(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (2(4(2e^(-1(-1x + 2)) - 1)^2 - 5(2e^(-1(-1x + 2)) - 1) + 5) + 2)/(-3(4(2e^(-1(-1x + 2)) - 1)^2 - 5(2e^(-1(-1x + 2)) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1sin(1\u03c0(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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3(1|((1(-1e^(1x) + 3) + 1)/(-3(-1e^(1x) + 3) + 1)) - 2|)^2 - 4(1|((1(-1e^(1x) + 3) + 1)/(-3(-1e^(1x) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3((3(1x^2 + 4x + 5) - 1)/(-2(1x^2 + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1(-4(1cos(2\u03c0x + 1) - 3) + 4)^2 - 4(-4(1cos(2\u03c0x + 1) - 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) = -2sin(1\u03c0((-3x - 2)/(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 maxima of the function f(x) = 1|(2(-4((3x + 1)/(3x - 2)) - 1)^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": "Find the average of all x-coordinates of local minima of the function f(x) = -2|(-2(-4x^2 - 4x + 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 extremum of the function f(x) = 1e^(1(1x^2 + 5x + 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) = 1|(4x^2 - 2x + 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 extremum with the smallest y-value of the function f(x) = 2|(1cos(1\u03c0x + 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 rightmost local extremum of the function f(x) = -2|((1(3sin(1\u03c0(5x^2 + 4x + 4) - 3) - 1) + 2)/(3(3sin(1\u03c0(5x^2 + 4x + 4) - 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 average of all x-coordinates of local maxima of the function f(x) = 2sin(2\u03c0(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": "How many local maxima does the function f(x) = 2|(-1x^2 - 2x) - 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) = -3(-1|(2((1x - 2)/(3x + 1))^2 - 1((1x - 2)/(3x + 1)) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(-3x - 1) + 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) = -3|(-3sin(1\u03c0(-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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 3(2(2|((2x - 2)/(-2x + 3)) + 3| - 2) - 1)^2 - 4(2(2|((2x - 2)/(-2x + 3)) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1((1(-2sin(3\u03c0(1|x + 2| + 1)) - 3) - 1)/(1(-2sin(3\u03c0(1|x + 2| + 1)) - 3) + 1)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4(-2e^(-1x) + 2)^2 + 4(-2e^(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(2x)^2 + 5(2x) - 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) = 2e^(-1(-4(2|x| - 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 rightmost local maximum of the function f(x) = -1((-2(1(2sin(2\u03c0x) + 1)^2 + 5(2sin(2\u03c0x) + 1) + 3) - 3)/(-1(1(2sin(2\u03c0x) + 1)^2 + 5(2sin(2\u03c0x) + 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": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-3|x - 3| + 2) + 2)/(1(-3|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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3sin(2\u03c0(-1|x| + 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": "How many local extrema (both minima and maxima) does the function f(x) = 2sin(3\u03c0(5(2x^2 + 2x + 2) - 4) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-2e^(-2((-3(4x^2 + 5x + 5) - 2)/(-3(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -4(-1|(-5x - 3) + 3| - 1)^2 + 4(-1|(-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 minimum with the largest y-value of the function f(x) = -3(-4(-2cos(1\u03c0(-1|x| - 1) - 2) - 2)^2 + 3(-2cos(1\u03c0(-1|x| - 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2|x|)^2 + 3(2|x|) 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|(-2(-4x - 1)^2 + 4(-4x - 1) - 5) + 2| + 3) + 3)/(2(2|(-2(-4x - 1)^2 + 4(-4x - 1) - 5) + 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) = 5(1e^(1x))^2 - 5(1e^(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2(2|(5((-3x + 2)/(-1x - 1)) - 3) - 3| - 2)^2 - 3(2|(5((-3x + 2)/(-1x - 1)) - 3) - 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 x-coordinate of the rightmost local maximum of the function f(x) = -2((1(1cos(2\u03c0x + 1)) + 2)/(2(1cos(2\u03c0x + 1)) - 3))^2 + 5((1(1cos(2\u03c0x + 1)) + 2)/(2(1cos(2\u03c0x + 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": "How many local extrema (both minima and maxima) does the function f(x) = 2cos(1\u03c0(3|x + 2| - 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4((-1(1(1|x - 1| - 3)^2 - 1(1|x - 1| - 3) - 5) - 3)/(2(1(1|x - 1| - 3)^2 - 1(1|x - 1| - 3) - 5) + 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 rightmost local maximum of the function f(x) = 2|(3cos(3\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 x-coordinate of the local maximum of the function f(x) = (1(1|(-2e^(1x) + 3) - 1| - 3) + 3)/(3(1|(-2e^(1x) + 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": "0", "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(5(2|x| - 1)^2 - 2(2|x| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 5(1cos(3\u03c0x - 2))^2 - 3(1cos(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-4x)| - 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 maxima does the function f(x) = 2((1x - 1)/(2x + 2))^2 + 2((1x - 1)/(2x + 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 of the function f(x) = -1(-1|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 rightmost local minimum of the function f(x) = 2sin(2\u03c0(-1((1x + 2)/(1x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (3(3|(4(-4x - 3)^2 - 1) - 3| - 2))/(-1(3|(4(-4x - 3)^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|(3cos(3\u03c0(-2(-1x + 3)^2 - 1(-1x + 3) - 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": "How many local maxima does the function f(x) = 4(-1(-2|((-3x + 2)/(-1x + 2))| + 1) - 2)^2 - 1(-1(-2|((-3x + 2)/(-1x + 2))| + 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 with the smallest y-value of the function f(x) = 2(5((2(-3cos(2\u03c0x + 1) - 3) + 1)/(2(-3cos(2\u03c0x + 1) - 3) - 3))^2 + 4((2(-3cos(2\u03c0x + 1) - 3) + 1)/(2(-3cos(2\u03c0x + 1) - 3) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1(-1cos(3\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (3(-2x^2 + 1x + 3))/(-2(-2x^2 + 1x + 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 average of all x-coordinates of local maxima of the function f(x) = 1|(2cos(1\u03c0(5x) + 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 maximum of the function f(x) = (-2(4(-2|x - 2| + 3)^2 - 1(-2|x - 2| + 3) - 3) - 2)/(3(4(-2|x - 2| + 3)^2 - 1(-2|x - 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 extremum with the largest y-value of the function f(x) = (3(3e^(-2(1x^2 + 2x + 4)) + 2) + 2)/(-1(3e^(-2(1x^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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4(-5(-2|x + 3| - 2))^2 - 1(-5(-2|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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1((-2(-4x^2 - 3x - 4) + 3)/(-3(-4x^2 - 3x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4(3(3cos(3\u03c0x + 2) - 2)^2 - 5(3cos(3\u03c0x + 2) - 2) - 4) - 3 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 extremum with the smallest y-value of the function f(x) = -2sin(3\u03c0(-2|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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2|(4(3cos(3\u03c0x + 2)) - 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 x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1((2x - 1)/(-3x + 1))^2 - 3((2x - 1)/(-3x + 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) = -2cos(2\u03c0((-3(-3|(1x - 3) + 2| - 3) - 1)/(-2(-3|(1x - 3) + 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 extremum of the function f(x) = (-2(-3x^2 - 4x + 1))/(-2(-3x^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 leftmost local extremum of the function f(x) = 4(-3|(-4(-3e^(-1x))^2 - 3(-3e^(-1x)) + 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": "How many local minima does the function f(x) = 1|(2(2e^(1(-3x - 5)) - 1)^2 + 3(2e^(1(-3x - 5)) - 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 average of all x-coordinates of local maxima of the function f(x) = -3sin(3\u03c0(3|((-2(-3x^2 - 4x + 1) - 2)/(2(-3x^2 - 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 with the largest y-value of the function f(x) = 3e^(-1(5(5(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1cos(3\u03c0(4((3(3x^2 - 2x + 2) + 2)/(-1(3x^2 - 2x + 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": "-2", "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 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((3x)/(1x + 3))^2 - 3((3x)/(1x + 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": "How many local extrema (both minima and maxima) does the function f(x) = -1(-1(3|((3x - 1)/(-3x + 2)) - 2|)^2 + 2(3|((3x - 1)/(-3x + 2)) - 2|) - 4) 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": "Find the average of all x-coordinates of local minima of the function f(x) = 1|((-2(3sin(3\u03c0(-3x^2 - 1x - 4) + 2) + 1))/(2(3sin(3\u03c0(-3x^2 - 1x - 4) + 2) + 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 minimum with the largest y-value of the function f(x) = -1|(-1sin(2\u03c0(-5((-1x + 1)/(2x + 1))^2 - 5((-1x + 1)/(2x + 1)) - 2) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5((2(-3(-2|x| - 2) - 1) - 3)/(-1(-3(-2|x| - 2) - 1) - 1))^2 + 3((2(-3(-2|x| - 2) - 1) - 3)/(-1(-3(-2|x| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3cos(1\u03c0((-3(-2|x| + 3) - 1)/(-1(-2|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": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1cos(2\u03c0(4x^2 - 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 extremum with the smallest y-value of the function f(x) = 2(3|x| - 3)^2 + 5(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-1(5(3cos(1\u03c0(-3x^2) + 1) + 3) - 3))/(3(5(3cos(1\u03c0(-3x^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 minimum of the function f(x) = 1|(1(1x^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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1sin(2\u03c0(-4x^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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 4(3|(2cos(3\u03c0((-1x + 3)/(-2x + 3)) - 1) + 3)|)^2 + 1(3|(2cos(3\u03c0((-1x + 3)/(-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": "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(3sin(1\u03c0(2x^2 - 3x - 2) - 2) - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-3(3(2|(5x)| - 1)^2 + 3(2|(5x)| - 1)) - 2)/(1(3(2|(5x)| - 1)^2 + 3(2|(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|((-2(2x^2 - 2x + 3) + 2)/(-1(2x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(3|x - 3| - 3))/(2(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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|((2(-5x^2 - 4x + 4) + 2)/(-3(-5x^2 - 4x + 4) + 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 of the function f(x) = -3e^(2((-2x + 1)/(-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 leftmost local maximum of the function f(x) = 1cos(2\u03c0(-4x^2 - 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": "-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|((3(1sin(2\u03c0x + 2) - 1) - 3)/(-1(1sin(2\u03c0x + 2) - 1) + 3)) + 3| + 2)^2 + 1(-1|((3(1sin(2\u03c0x + 2) - 1) - 3)/(-1(1sin(2\u03c0x + 2) - 1) + 3)) + 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 local extremum with the smallest y-value of the function f(x) = -2|(-2(3sin(2\u03c0x + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|((2(3x^2 - 4x + 4))/(1(3x^2 - 4x + 4) - 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 leftmost local minimum of the function f(x) = (-2(-2|(2sin(1\u03c0x + 2) - 1) + 3| - 2) - 2)/(-3(-2|(2sin(1\u03c0x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|((-1(3(-2x + 5)^2 + 4(-2x + 5) + 2) + 3)/(-2(3(-2x + 5)^2 + 4(-2x + 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": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3(-2sin(3\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) = (1(1(2|(1x^2 + 3x - 4) + 3|) + 5) - 3)/(1(1(2|(1x^2 + 3x - 4) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1cos(2\u03c0((3(-1|x - 2| + 3) + 2)/(1(-1|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3(-3sin(2\u03c0x + 3) + 2)^2 - 5(-3sin(2\u03c0x + 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 local extremum with the smallest y-value of the function f(x) = -5(-2sin(2\u03c0(-1x + 2)) + 1)^2 - 3(-2sin(2\u03c0(-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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-1(-1cos(3\u03c0(2(-2|x + 1| + 2) + 1) + 2) + 3) + 1)/(1(-1cos(3\u03c0(2(-2|x + 1| + 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": "-10", "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(-2|((2(2x^2 + 4x + 5))/(-3(2x^2 + 4x + 5) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5((3(-1(-2|x| + 1)^2 + 1) - 3)/(-2(-1(-2|x| + 1)^2 + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(-2(-3|x - 3| - 2)^2 - 5(-3|x - 3| - 2) - 2) + 2)/(-3(-2(-3|x - 3| - 2)^2 - 5(-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 of the function f(x) = 2e^(2((1(-2|(-3x - 2) + 2| - 3) + 2)/(-2(-2|(-3x - 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": "Find the x-coordinate of the local maximum of the function f(x) = -4((1(2x - 1) + 3)/(1(2x - 1)))^2 + 2((1(2x - 1) + 3)/(1(2x - 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|(5((-2x - 3)/(-3x - 2))^2 + 3((-2x - 3)/(-3x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(1(2cos(2\u03c0x + 2) + 3) + 1) + 2)/(1(1(2cos(2\u03c0x + 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": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(-3(-1sin(3\u03c0(-3x^2 + 5x - 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": "How many local maxima does the function f(x) = -4(-4(-2|x + 3| + 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 rightmost local maximum of the function f(x) = -3e^(1(-3|x - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|((3(-1(-4x + 1)^2 + 5(-4x + 1) + 5) - 1)/(-3(-1(-4x + 1)^2 + 5(-4x + 1) + 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 local minimum with the smallest y-value of the function f(x) = -4(3cos(2\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (1(-3e^(-2(5x - 5)) - 3))/(3(-3e^(-2(5x - 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 average of all x-coordinates of local minima of the function f(x) = -1e^(1(-1|(-1(-2x + 4)^2 + 5(-2x + 4) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1(2|x + 1| - 3)^2 + 4(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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1sin(1\u03c0(-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": "-8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(-4(-1x^2 - 4x + 4) - 5) - 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 smallest y-value of the function f(x) = 1|(-1(2((-2x + 1)/(2x + 2))^2 + 5((-2x + 1)/(2x + 2)) + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(3cos(1\u03c0x + 1) + 2)^2 + 3(3cos(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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5((-3(-2e^(-1x) + 3) - 2)/(3(-2e^(-1x) + 3) + 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1(-2(1sin(3\u03c0x) - 2)^2 - 5(1sin(3\u03c0x) - 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": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1sin(2\u03c0(-2((1(1|x + 2| - 3) + 3)/(3(1|x + 2| - 3) - 2)) - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3sin(1\u03c0(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3sin(1\u03c0(1(-2|x + 2| - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(-1|(2(-2e^(-1x) + 1) + 1) + 2| + 2)^2 + 1(-1|(2(-2e^(-1x) + 1) + 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 local maximum with the largest y-value of the function f(x) = (-3(5(1(3cos(2\u03c0x) - 3) - 1)^2 + 4(1(3cos(2\u03c0x) - 3) - 1) - 3) + 3)/(1(5(1(3cos(2\u03c0x) - 3) - 1)^2 + 4(1(3cos(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": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(-5x^2 - 5x + 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) = -2|(-3(1cos(3\u03c0x - 2) - 2)^2 - 2(1cos(3\u03c0x - 2) - 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1sin(1\u03c0((-2(-3|x - 2| - 2) + 1)/(1(-3|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2sin(3\u03c0((-1(-5x^2 + 3x + 3) - 2)/(-2(-5x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(-4x^2 - 5x + 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 extremum with the smallest y-value of the function f(x) = -2e^(-2(-5(1x + 1)^2 - 5(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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(-2(-1x^2 + 1x + 2) + 4) + 2)/(1(-2(-1x^2 + 1x + 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 leftmost local maximum of the function f(x) = 3(-2e^(1(-2|(-5x - 2) - 1| - 1)))^2 + 3(-2e^(1(-2|(-5x - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2(-1|x + 2|)^2 + 1(-1|x + 2|) - 4 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 maximum with the smallest y-value of the function f(x) = 3e^(1(-3|(-5((-2x + 1)/(-2x - 1))^2 - 5((-2x + 1)/(-2x - 1)) - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(3|(-5x^2 + 3x) - 1|) + 1)/(-2(3|(-5x^2 + 3x) - 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) = -2e^(-1((-2(2x + 1) - 3)/(-3(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 leftmost local minimum of the function f(x) = (-2(-1(-1(-1sin(3\u03c0x + 2) + 2))^2 + 5(-1(-1sin(3\u03c0x + 2) + 2)) - 5) + 1)/(1(-1(-1(-1sin(3\u03c0x + 2) + 2))^2 + 5(-1(-1sin(3\u03c0x + 2) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1(2|(3x^2 - 2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(2x + 2)^2 - 2(2x + 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(-1(1e^(-2x) - 2)^2 + 5(1e^(-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": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 5(-2sin(2\u03c0((-2(-1x^2 + 1x - 5) - 3)/(-1(-1x^2 + 1x - 5) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-3((-3(-3x + 5) + 2)/(2(-3x + 5) - 3))^2 - 5((-3(-3x + 5) + 2)/(2(-3x + 5) - 3)) - 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 of the function f(x) = 3((2(-3x^2 - 2x - 5) + 3)/(-2(-3x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(2x^2 - 3x - 5) - 2)/(-3(2x^2 - 3x - 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 minimum of the function f(x) = -4(-3x^2 + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2|((-2(3cos(1\u03c0(-1x + 2) - 3) + 1))/(3(3cos(1\u03c0(-1x + 2) - 3) + 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 local maximum with the smallest y-value of the function f(x) = 2(3(-3cos(3\u03c0(-3|x + 3| + 3) + 3) + 2)^2 + 2(-3cos(3\u03c0(-3|x + 3| + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (2(3cos(1\u03c0x + 3) + 1) - 2)/(-2(3cos(1\u03c0x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2((1(5x - 5) + 1)/(-3(5x - 5) + 4))^2 + 1((1(5x - 5) + 1)/(-3(5x - 5) + 4)) - 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 minimum of the function f(x) = -3e^(1(-3x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|(-4x^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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(3sin(3\u03c0(-5x^2 + 1x + 5) + 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 extremum of the function f(x) = -2|(-5(5x + 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": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1cos(1\u03c0(-1|(4x^2 - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3cos(2\u03c0(3(2((-3x + 1)/(-3x - 3))^2 + 3((-3x + 1)/(-3x - 3)) + 1) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -4((-1x + 1)/(-1x))^2 + 4((-1x + 1)/(-1x)) + 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 average of all x-coordinates of local maxima of the function f(x) = -2((-1(-1cos(2\u03c0(1x - 1)) + 2) + 3)/(-2(-1cos(2\u03c0(1x - 1)) + 2) + 3))^2 - 5((-1(-1cos(2\u03c0(1x - 1)) + 2) + 3)/(-2(-1cos(2\u03c0(1x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3(1x)^2 - 3(1x) - 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) = (-3(3|(-2(-3x + 3)^2 - 1(-3x + 3) + 2) + 3| + 1) + 2)/(-1(3|(-2(-3x + 3)^2 - 1(-3x + 3) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|((2(2cos(3\u03c0(-4x) - 1) + 3))/(3(2cos(3\u03c0(-4x) - 1) + 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 minimum of the function f(x) = 3|(-1((-2(-5x^2 - 5x + 2) + 1)/(2(-5x^2 - 5x + 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": "0", "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((-2(3|x - 3| + 3) - 3)/(-1(3|x - 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 of the function f(x) = 4(5(-2|((3x)/(-1x - 3)) - 2| - 2)^2 + 5(-2|((3x)/(-1x - 3)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-1(-3(-5(2|x + 1| - 1)^2 - 3(2|x + 1| - 1) - 5) + 1) + 2)/(3(-3(-5(2|x + 1| - 1)^2 - 3(2|x + 1| - 1) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(-1cos(3\u03c0x - 1) - 2)^2 + 1(-1cos(3\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": "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(2\u03c0x + 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 minimum of the function f(x) = 5(2|x - 3| + 2)^2 + 5(2|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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2cos(2\u03c0(3((1(-5x^2 - 3x + 2) - 1)/(1(-5x^2 - 3x + 2) + 3)) - 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 minimum with the smallest y-value of the function f(x) = 1cos(3\u03c0(-2(1|((-1x)/(-1x + 2))| + 2)^2 - 2(1|((-1x)/(-1x + 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": "Find the x-coordinate of the local minimum of the function f(x) = 1((-2x - 2)/(-2x + 3))^2 + 3((-2x - 2)/(-2x + 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": "Find the x-coordinate of the local extremum of the function f(x) = -5(2|(-4((2x + 3)/(-1x + 3))^2 + 1((2x + 3)/(-1x + 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 rightmost local minimum of the function f(x) = 2sin(3\u03c0(-2((3(2|x - 3| - 2) + 3)/(1(2|x - 3| - 2) - 3))^2 + 3((3(2|x - 3| - 2) + 3)/(1(2|x - 3| - 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 maximum of the function f(x) = -2(1|((-3(-5x^2 + 1x - 4) + 3)/(3(-5x^2 + 1x - 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(2x^2 - 3x - 3) + 3)/(2(2x^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": "How many local minima does the function f(x) = -4((2(-1x) + 1)/(2(-1x) + 2))^2 - 5((2(-1x) + 1)/(2(-1x) + 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) = 1((-3(3|(-5x^2 + 3x - 5) - 3| - 2))/(3(3|(-5x^2 + 3x - 5) - 3| - 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 average of all x-coordinates of local minima of the function f(x) = 2((-2(-1(1|x - 2| - 2) - 1) - 2)/(-1(-1(1|x - 2| - 2) - 1) - 2))^2 - 2((-2(-1(1|x - 2| - 2) - 1) - 2)/(-1(-1(1|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3(5((1x - 2)/(3x)) - 5)^2 + 5(5((1x - 2)/(3x)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1((3(3|x - 1| + 1) - 3)/(-3(3|x - 1| + 1) + 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 average of all x-coordinates of local extrema of the function f(x) = -5(3cos(1\u03c0(1|x - 2|) - 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": "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(-3|(-1x^2 - 2x - 2) + 3| + 2) + 4) - 2)/(1(2(-3|(-1x^2 - 2x - 2) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|((2(-4(-3x^2 - 1)))/(1(-4(-3x^2 - 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 maximum with the smallest y-value of the function f(x) = 1(2sin(1\u03c0(-4((2x + 3)/(-2x))^2 - 5((2x + 3)/(-2x)) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(-1|(2cos(1\u03c0x) + 1) + 3| - 2) - 3)/(3(-1|(2cos(1\u03c0x) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3((-1(-2x^2 - 3x - 2) + 3)/(2(-2x^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(3((1(-4x - 2) + 3)/(-2(-4x - 2) + 3))^2 + 1((1(-4x - 2) + 3)/(-2(-4x - 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 local extremum of the function f(x) = (1(2(-5x + 5)^2 - 5(-5x + 5) + 2))/(2(2(-5x + 5)^2 - 5(-5x + 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 rightmost local maximum of the function f(x) = (-2(-3(5(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 4) - 2) + 3)/(-2(-3(5(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 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": "How many local maxima does the function f(x) = -3|((-1(1(-3sin(2\u03c0x) - 2) - 2) - 2)/(-2(1(-3sin(2\u03c0x) - 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 x-coordinate of the local extremum of the function f(x) = -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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4(2|((1(-2x^2 + 4x - 2) - 3)/(3(-2x^2 + 4x - 2) + 1)) - 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": "How many local minima does the function f(x) = (-2(-3|(-3x^2 - 5x + 1) + 3| - 3) - 3)/(-2(-3|(-3x^2 - 5x + 1) + 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 leftmost local maximum of the function f(x) = -5(2cos(1\u03c0((-3x - 2)/(-3x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(1(-1(-1x^2 + 5x - 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": "How many local extrema (both minima and maxima) does the function f(x) = -2(4(-1sin(3\u03c0x + 1) + 2)^2 + 1(-1sin(3\u03c0x + 1) + 2) - 4) - 4 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 x-coordinate of the local minimum of the function f(x) = 1((2x - 1)/(-3x + 4))^2 - 5((2x - 1)/(-3x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|(-4(3((-3x)/(2x)) - 1)^2 - 1(3((-3x)/(2x)) - 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -5(-2cos(2\u03c0((2(-2|x - 3| - 1) - 3)/(-3(-2|x - 3| - 1) - 2)) - 2) + 1)^2 - 5(-2cos(2\u03c0((2(-2|x - 3| - 1) - 3)/(-3(-2|x - 3| - 1) - 2)) - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(-2(3e^(-1(5x^2 - 2x + 3)) + 1) + 4))/(-3(-2(3e^(-1(5x^2 - 2x + 3)) + 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 maximum of the function f(x) = -2(2|((2(-4x^2 - 1x - 4))/(2(-4x^2 - 1x - 4) - 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 local minimum with the smallest y-value of the function f(x) = 4(-3|(-4x + 1) - 2| + 1)^2 + 4(-3|(-4x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3|(-4x - 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 maximum of the function f(x) = -3|(-2cos(2\u03c0x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(4(-1sin(3\u03c0(-1|x - 3|) + 1) + 3)^2 + 3) - 2)/(-1(4(-1sin(3\u03c0(-1|x - 3|) + 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 local extremum of the function f(x) = -3|(-4((-1(3x - 5))/(2(3x - 5) - 3))^2 - 5((-1(3x - 5))/(2(3x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1e^(1(1x^2 - 3x + 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 average of all x-coordinates of local maxima of the function f(x) = 2|(2((-1(2cos(3\u03c0x + 3)) - 1)/(1(2cos(3\u03c0x + 3)) + 2)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (3(2|(2(2x^2 - 3x - 4) + 3) + 1|) - 3)/(2(2|(2(2x^2 - 3x - 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 x-coordinate of the leftmost local maximum of the function f(x) = -1e^(2(3(3|(4x^2 + 2x - 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": "How many local maxima does the function f(x) = 1(-1|x + 3| + 2)^2 + 5(-1|x + 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 x-coordinate of the local extremum with the largest y-value of the function f(x) = (-2(-1(3sin(2\u03c0(-5x^2 + 5x - 4) + 1) + 3) + 3) - 3)/(1(-1(3sin(2\u03c0(-5x^2 + 5x - 4) + 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 minimum of the function f(x) = 1(3cos(2\u03c0x + 3) - 3)^2 + 5(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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1cos(1\u03c0(4(3|((3x + 3)/(3x - 2)) - 2| + 2) - 1) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3cos(1\u03c0(1|(-4x + 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 largest y-value of the function f(x) = -4(1|(-1cos(2\u03c0(-2x - 3) + 3) + 1) + 2| - 1)^2 + 1(1|(-1cos(2\u03c0(-2x - 3) + 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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-2(1(-1(-2cos(1\u03c0x + 1) + 2)^2 - 5) - 3) - 1)/(-3(1(-1(-2cos(1\u03c0x + 1) + 2)^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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(-5x^2 - 5x + 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) = 2e^(-1(-3((-1x)/(-3x + 4))^2 + 2((-1x)/(-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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(-3|((-2x + 1)/(-2x)) + 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) = 2(2|(2sin(1\u03c0x + 3) + 1) + 1| - 3)^2 - 4(2|(2sin(1\u03c0x + 3) + 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 extremum of the function f(x) = -2|(5((-1(-4x^2 + 4x - 5) - 3)/(1(-4x^2 + 4x - 5) + 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 maxima does the function f(x) = 1|(-2x^2 - 5x - 5) - 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 of the function f(x) = -3e^(-2(-1|(-3((-1x + 3)/(1x + 2))^2 + 3((-1x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(1|((2x)/(1x - 3)) - 1| - 1)^2 + 1(1|((2x)/(1x - 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 rightmost local maximum of the function f(x) = -2sin(1\u03c0((-2x + 1)/(-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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3|(2(3sin(2\u03c0x + 3))^2 - 4(3sin(2\u03c0x + 3)) + 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": "How many local maxima does the function f(x) = 3(2e^(-2(-3|(1x + 3)| - 1)) - 2)^2 - 1(2e^(-2(-3|(1x + 3)| - 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 maximum with the smallest y-value of the function f(x) = -2sin(1\u03c0((-3x - 3)/(-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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1cos(1\u03c0(1|((3(5x^2 + 1x - 2) - 1)/(-3(5x^2 + 1x - 2) - 2)) + 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": "Find the average of all x-coordinates of local maxima of the function f(x) = -4(1|(1(3cos(1\u03c0x + 3) - 2) - 3) - 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": "How many local minima does the function f(x) = -2e^(1(2|x - 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) = 3((3x)/(1x - 3))^2 - 2((3x)/(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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(-4((-1(2|x - 1| - 1) + 1)/(2(2|x - 1| - 1) - 1))^2 - 3((-1(2|x - 1| - 1) + 1)/(2(2|x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(2sin(2\u03c0x) + 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) = -1sin(3\u03c0((3x - 3)/(3x - 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) = -3|(2sin(3\u03c0x + 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": "-10", "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((3(-2|x| - 3))/(-3(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1|(-3(1((3x - 2)/(-2x - 3)) - 4)^2 + 1(1((3x - 2)/(-2x - 3)) - 4) - 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 minimum with the smallest y-value of the function f(x) = 3cos(1\u03c0(5x^2 - 3x + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2sin(3\u03c0(-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 local maximum of the function f(x) = 3((-1(-2|(-1x^2 - 5x + 3) + 3| - 2) + 1)/(2(-2|(-1x^2 - 5x + 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": "-2", "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(3\u03c0(-1x^2 - 5x - 1) - 3) + 2))/(-2(2cos(3\u03c0(-1x^2 - 5x - 1) - 3) + 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 local minimum with the smallest y-value of the function f(x) = -1sin(2\u03c0(4x^2 + 2x + 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(2x^2 + 3x - 3))/(1(2x^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(2sin(3\u03c0(-5(2x - 1)^2 - 4))) + 3)/(-3(2sin(3\u03c0(-5(2x - 1)^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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-3(-3|(-5(2x - 1)^2 + 5(2x - 1) + 3) + 3| - 2))/(-1(-3|(-5(2x - 1)^2 + 5(2x - 1) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(1(-2|(-1cos(1\u03c0x - 1) - 2) - 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 largest y-value of the function f(x) = (-1(2(4(3|x + 3| - 2)^2 + 4(3|x + 3| - 2) - 5) - 3) + 2)/(2(2(4(3|x + 3| - 2)^2 + 4(3|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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(1sin(3\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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-5x^2 - 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) = -1(-1cos(2\u03c0((1(-1x - 2) - 2)/(-1(-1x - 2) + 3)) - 3) + 3)^2 + 4(-1cos(2\u03c0((1(-1x - 2) - 2)/(-1(-1x - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|(-3x^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 minimum with the smallest y-value of the function f(x) = 3sin(1\u03c0(-2x^2 - 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": "-10", "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(2|(2x^2 - 3x - 2) - 1| - 2) + 2)/(1(2|(2x^2 - 3x - 2) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1e^(2(-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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(5(3sin(2\u03c0x - 3) + 3) - 5) - 2)/(2(5(3sin(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": "Find the x-coordinate of the local minimum of the function f(x) = (-1(-3(1x^2 - 5x - 4)) + 3)/(2(-3(1x^2 - 5x - 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 local minimum of the function f(x) = -2|((1(-5x) - 1)/(-3(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(-3cos(2\u03c0((1x - 1)/(-3x)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(-2(2x + 1)^2 - 3(2x + 1) + 1) - 2)/(-1(-2(2x + 1)^2 - 3(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (3(3(5(-2|x + 3| + 2)^2 + 3(-2|x + 3| + 2)) - 4) - 3)/(-3(3(5(-2|x + 3| + 2)^2 + 3(-2|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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5((-3(-1(1|x + 1| - 3)^2 - 1(1|x + 1| - 3)) + 2)/(2(-1(1|x + 1| - 3)^2 - 1(1|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 average of all x-coordinates of local extrema of the function f(x) = 5(-1|((1(-2x - 5) - 3)/(-1(-2x - 5) + 2)) + 3| + 3)^2 + 5(-1|((1(-2x - 5) - 3)/(-1(-2x - 5) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3((1(2(-2|x| + 2)^2 - 3(-2|x| + 2) - 2) - 3)/(3(2(-2|x| + 2)^2 - 3(-2|x| + 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": "How many local extrema (both minima and maxima) does the function f(x) = -1sin(3\u03c0((-1(2(3|x - 3|) - 4) + 1)/(2(2(3|x - 3|) - 4) - 1))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(-4(3|(-2x^2 - 3x + 4)| - 2) - 2) - 1)/(2(-4(3|(-2x^2 - 3x + 4)| - 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 maximum of the function f(x) = 1cos(2\u03c0((-2x + 1)/(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3(-2|(-2sin(2\u03c0((-1x - 1)/(1x)) + 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1sin(2\u03c0(-4x^2 - 5x - 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 extremum of the function f(x) = (-3(2(-1x^2 + 2x - 1)) - 1)/(-2(2(-1x^2 + 2x - 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) = 3|((1(-4(2sin(3\u03c0x) + 3) - 2) - 3)/(-1(-4(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 leftmost local minimum of the function f(x) = -2((-3(-3(-3sin(3\u03c0x - 2) + 1)^2 - 3(-3sin(3\u03c0x - 2) + 1) + 4) - 1)/(-1(-3(-3sin(3\u03c0x - 2) + 1)^2 - 3(-3sin(3\u03c0x - 2) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2|(3cos(1\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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(-3(1|x - 2| + 2)^2 + 5(1|x - 2| + 2) + 4))/(3(-3(1|x - 2| + 2)^2 + 5(1|x - 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": "2", "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(-3|x + 3| + 1)^2 + 3(-3|x + 3| + 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 rightmost local extremum of the function f(x) = 1|(-5(-1sin(1\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 extremum of the function f(x) = (-1(3x^2 - 1x - 1) + 3)/(-1(3x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(3(2x^2 + 2x) + 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 maximum of the function f(x) = -2sin(3\u03c0(1|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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (1(2(1(2|x - 1| - 3)^2 - 3(2|x - 1| - 3) + 5) - 2) - 3)/(-1(2(1(2|x - 1| - 3)^2 - 3(2|x - 1| - 3) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(-5(-2e^(-2(-1|x - 1| - 3)) + 3) - 5)^2 + 3(-5(-2e^(-2(-1|x - 1| - 3)) + 3) - 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": "1", "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((2(5(-2x^2 - 2x + 4) + 5))/(1(5(-2x^2 - 2x + 4) + 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 extremum with the largest y-value of the function f(x) = -2(3(-2cos(2\u03c0((-3x + 1)/(-2x + 3)) - 2))^2 + 3(-2cos(2\u03c0((-3x + 1)/(-2x + 3)) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(2\u03c0(4x + 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) = (1(1|(3x - 1)| - 1) + 3)/(1(1|(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 average of all x-coordinates of local minima of the function f(x) = -3((-3(-2|(-1x^2 - 2x + 3)| + 1) + 2)/(-3(-2|(-1x^2 - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(1(-2x^2 + 2x - 4) - 4) + 3)/(2(1(-2x^2 + 2x - 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 minimum with the largest y-value of the function f(x) = 3sin(3\u03c0(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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2sin(3\u03c0(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3sin(3\u03c0(-3|((1(-3x - 5))/(3(-3x - 5) - 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 average of all x-coordinates of local minima of the function f(x) = 1(1|((-1(-2x + 3) + 2)/(2(-2x + 3) + 3)) + 2| + 2)^2 - 5(1|((-1(-2x + 3) + 2)/(2(-2x + 3) + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5(-1cos(2\u03c0x - 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": "How many local minima does the function f(x) = -2sin(1\u03c0((-3(-1|x + 2|))/(-2(-1|x + 2|) + 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 maximum of the function f(x) = 4(-5x^2 + 1x - 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 extremum of the function f(x) = -4((-1(1x - 1) - 1)/(3(1x - 1) - 1))^2 + 3((-1(1x - 1) - 1)/(3(1x - 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 extremum of the function f(x) = -1((1(2(-1|x + 2|)^2 + 4))/(2(2(-1|x + 2|)^2 + 4) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3(5x^2 - 4) - 2)/(-1(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(3x^2 - 3x - 1) + 3)/(-2(3x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2cos(1\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": "How many local minima does the function f(x) = (1(-1x^2 + 4x - 2))/(1(-1x^2 + 4x - 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) = 2sin(2\u03c0((3(-3|(-4x^2 - 5) - 1| - 3) + 3)/(2(-3|(-4x^2 - 5) - 1| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5(1|((-2(3x^2 - 1x))/(-1(3x^2 - 1x) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1e^(1(2(-3|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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2sin(3\u03c0(3|(-2((1x - 1)/(2x + 3))^2 + 4((1x - 1)/(2x + 3)) + 5) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1cos(3\u03c0(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) = (3(3(3|(-2cos(1\u03c0x - 1)) - 2| + 2)^2 + 5(3|(-2cos(1\u03c0x - 1)) - 2| + 2) - 3) + 3)/(-2(3(3|(-2cos(1\u03c0x - 1)) - 2| + 2)^2 + 5(3|(-2cos(1\u03c0x - 1)) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(-3((1x)/(-1x + 2))^2 - 3((1x)/(-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 of the function f(x) = 3((3x - 2)/(2x + 2))^2 + 2((3x - 2)/(2x + 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 extrema of the function f(x) = 2(-1|(-1((3x - 3)/(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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|(4(1((-2x - 1)/(-3x))^2 + 5((-2x - 1)/(-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": "How many local minima does the function f(x) = -3(2((-2x + 1)/(2x + 3))^2 + 3((-2x + 1)/(2x + 3)) + 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 minimum of the function f(x) = -4((2(-1|(-2x^2 - 2x + 3) + 1| + 3) + 3)/(2(-1|(-2x^2 - 2x + 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(-3x^2 - 2x + 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) = (2(-1sin(2\u03c0x - 2) - 3))/(2(-1sin(2\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 x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(3x^2 - 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": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(1(-1sin(3\u03c0(1x^2 - 3x) + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|((1(-1sin(1\u03c0(3x + 1) - 2) + 2) + 3)/(-3(-1sin(1\u03c0(3x + 1) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2(-1|((-3(1x + 1) + 2)/(-1(1x + 1) - 3))| + 2)^2 + 5(-1|((-3(1x + 1) + 2)/(-1(1x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(2(1((1x)/(2x + 2)) - 2)^2 - 3(1((1x)/(2x + 2)) - 2) - 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 with the largest y-value of the function f(x) = -3(2|(-1cos(3\u03c0x - 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 x-coordinate of the leftmost local maximum of the function f(x) = (1(-5(-1sin(2\u03c0x) + 2)^2 + 4(-1sin(2\u03c0x) + 2) - 3) + 3)/(-1(-5(-1sin(2\u03c0x) + 2)^2 + 4(-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 leftmost local minimum of the function f(x) = -1|(-4(3((-2x + 3)/(1x)) + 1)^2 - 4(3((-2x + 3)/(1x)) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3e^(1(-1|x|)) - 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|(-1(4x + 4)^2 + 4(4x + 4) + 2) - 3| + 3) + 2)/(-3(1|(-1(4x + 4)^2 + 4(4x + 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(5(1(-1|x|)^2 + 4(-1|x|) + 3) + 2) - 1)/(3(5(1(-1|x|)^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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2cos(1\u03c0(-5x^2 - 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 extremum with the largest y-value of the function f(x) = -1e^(1(-2|((-1x - 1)/(-2x - 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) = -2e^(2(3((-2(-2|x + 3| + 3) - 2)/(-3(-2|x + 3| + 3) + 2))^2 - 5((-2(-2|x + 3| + 3) - 2)/(-3(-2|x + 3| + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2sin(1\u03c0(2(1|x| - 3)^2 - 3(1|x| - 3) - 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 with the largest y-value of the function f(x) = -2cos(3\u03c0(-3x^2 - 4x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(5x^2 + 4x - 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|((3(-3x^2 - 2) + 1)/(3(-3x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-1e^(2x) + 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 average of all x-coordinates of local extrema of the function f(x) = 2|(-1cos(3\u03c0x - 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(2|(-5(-1sin(1\u03c0x - 3))^2 + 1(-1sin(1\u03c0x - 3)) - 1)|) + 3)/(2(2|(-5(-1sin(1\u03c0x - 3))^2 + 1(-1sin(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1sin(1\u03c0(1(4x + 4)^2 - 3(4x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(3(2((-3x - 1)/(1x - 3))^2 - 4((-3x - 1)/(1x - 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": "How many local minima does the function f(x) = (1(4(-1|x - 1| + 3)^2 - 5(-1|x - 1| + 3) + 1) + 2)/(2(4(-1|x - 1| + 3)^2 - 5(-1|x - 1| + 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 average of all x-coordinates of local minima of the function f(x) = (3(-3|(5(-4x)^2 + 3(-4x) + 2) + 1| - 2))/(2(-3|(5(-4x)^2 + 3(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(2\u03c0(-2|x + 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 extremum of the function f(x) = -4(-3((-1x - 1)/(2x))^2 - 2((-1x - 1)/(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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(-1|((-3(-1x^2 - 4x + 4) - 2)/(1(-1x^2 - 4x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(1x^2 - 1x + 3) - 1)/(-1(1x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(-2e^(-2x) + 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) = -3cos(3\u03c0(-2x^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 extrema of the function f(x) = 1sin(3\u03c0(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 x-coordinate of the local minimum of the function f(x) = 3|(2(4((-2x)/(2x - 1))^2 + 4((-2x)/(2x - 1)) + 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 rightmost local minimum of the function f(x) = 4(-1cos(3\u03c0(1|((-1x - 1)/(3x + 2)) - 2| + 3) - 1) + 2)^2 - 4(-1cos(3\u03c0(1|((-1x - 1)/(3x + 2)) - 2| + 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 average of all x-coordinates of local maxima of the function f(x) = -1e^(2(-4((2x - 3)/(1x - 2))^2 + 4((2x - 3)/(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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(-3(-2cos(2\u03c0x + 2) + 1)^2 - 4(-2cos(2\u03c0x + 2) + 1) - 2) - 1)/(-3(-3(-2cos(2\u03c0x + 2) + 1)^2 - 4(-2cos(2\u03c0x + 2) + 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 minimum with the smallest y-value of the function f(x) = 1(4(3e^(2(1|x - 2| - 1)) - 3) + 4)^2 + 1(4(3e^(2(1|x - 2| - 1)) - 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": "How many local minima does the function f(x) = 3(-1e^(-1(1|x| - 3)))^2 - 5(-1e^(-1(1|x| - 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 maximum of the function f(x) = (3(-1(-4x - 3)^2 - 4(-4x - 3) - 3) - 3)/(2(-1(-4x - 3)^2 - 4(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|((3x - 3)/(3x)) - 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|(2((-2x + 2)/(-3x - 1))^2 + 3((-2x + 2)/(-3x - 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 rightmost local extremum of the function f(x) = (1(2(1sin(1\u03c0x + 1) - 1)^2 + 2(1sin(1\u03c0x + 1) - 1) + 1) - 1)/(-2(2(1sin(1\u03c0x + 1) - 1)^2 + 2(1sin(1\u03c0x + 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 leftmost local extremum of the function f(x) = (-1(4(-1sin(3\u03c0(-2|x - 1| + 2) + 2) + 2) - 2) - 3)/(1(4(-1sin(3\u03c0(-2|x - 1| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (1(-1cos(1\u03c0(1x^2 + 1x + 1) - 1) - 1) - 1)/(-3(-1cos(1\u03c0(1x^2 + 1x + 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 extrema of the function f(x) = 1|(-2sin(3\u03c0(-4x^2 + 3x - 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1cos(2\u03c0(1|(3(-5x + 4)^2 + 4(-5x + 4) + 4) - 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 leftmost local extremum of the function f(x) = 3|(-4(-2cos(3\u03c0(-3x^2 + 3x - 3) - 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3(1cos(3\u03c0(-1x^2 + 2x - 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 of the function f(x) = 1((-2x - 1)/(1x))^2 - 2((-2x - 1)/(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 x-coordinate of the leftmost local extremum of the function f(x) = -2|(-3(-3cos(3\u03c0(-3x + 4) + 1))^2 + 2(-3cos(3\u03c0(-3x + 4) + 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": "How many local maxima does the function f(x) = -2|(-2(1((3x + 1)/(1x + 2)) - 5)^2 + 4(1((3x + 1)/(1x + 2)) - 5) + 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 leftmost local minimum of the function f(x) = (3(2e^(1x) - 3) + 3)/(1(2e^(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"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2e^(-2(-2|x - 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 smallest y-value of the function f(x) = 3sin(2\u03c0(-3|x + 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": "How many local maxima does the function f(x) = 5(-2e^(-1(3x - 3)) + 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 leftmost local extremum of the function f(x) = -3e^(1(-3|(1x^2 + 4x - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2cos(3\u03c0(2(2x + 2)^2 - 4(2x + 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(3(-3|(-2e^(1x) - 1) + 2| + 3)^2 + 4(-3|(-2e^(1x) - 1) + 2| + 3) - 4) + 2)/(-3(3(-3|(-2e^(1x) - 1) + 2| + 3)^2 + 4(-3|(-2e^(1x) - 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": "How many local maxima does the function f(x) = 2e^(2((-2x + 1)/(2x))) - 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(1sin(1\u03c0x - 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": "How many local maxima does the function f(x) = 2((2x + 2)/(-3x))^2 + 5((2x + 2)/(-3x)) + 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 largest y-value of the function f(x) = (-2(2cos(1\u03c0x + 2) - 3) - 1)/(1(2cos(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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(-2(1cos(3\u03c0(3|x + 2|) - 2))^2 - 4(1cos(3\u03c0(3|x + 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 x-coordinate of the local minimum of the function f(x) = (2(5(3|x - 1| - 3)^2 + 3(3|x - 1| - 3) + 2) + 2)/(2(5(3|x - 1| - 3)^2 + 3(3|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 extrema (both minima and maxima) does the function f(x) = -3e^(2((-2x + 3)/(-2x + 1))) - 2 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 extrema (both minima and maxima) does the function f(x) = 4(1|((2(-3x + 2) - 2)/(1(-3x + 2))) + 1|)^2 + 3(1|((2(-3x + 2) - 2)/(1(-3x + 2))) + 1|) + 2 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": "Find the x-coordinate of the local maximum of the function f(x) = -5(-2|(-3e^(-1(1x^2 - 3x + 4)) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-2(2e^(-1(-5x - 5)) - 3) - 1)/(3(2e^(-1(-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": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(2cos(2\u03c0x - 3) + 2) + 3)/(-3(2cos(2\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(-1|x - 1| + 2)^2 + 5(-1|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 local minimum with the largest y-value of the function f(x) = -1(2cos(1\u03c0x) + 1)^2 + 2(2cos(1\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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(2(-2|(3x - 2) + 3| + 1)^2 - 4(-2|(3x - 2) + 3| + 1) + 5) - 3)/(-2(2(-2|(3x - 2) + 3| + 1)^2 - 4(-2|(3x - 2) + 3| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(-2sin(2\u03c0(-3x^2 + 4x + 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 maximum with the smallest y-value of the function f(x) = (-1(-2(1cos(2\u03c0(-2x - 2) - 1) + 3)^2 + 3(1cos(2\u03c0(-2x - 2) - 1) + 3) + 5) + 1)/(-1(-2(1cos(2\u03c0(-2x - 2) - 1) + 3)^2 + 3(1cos(2\u03c0(-2x - 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1e^(-1(1x^2 + 2x + 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 maxima does the function f(x) = -2(3|((-2(2x^2 + 5x + 4) + 1)/(-2(2x^2 + 5x + 4) - 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) = 2cos(1\u03c0((-1x + 1)/(-1x - 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 average of all x-coordinates of local minima of the function f(x) = -3sin(3\u03c0(-1(-2((2x - 3)/(-2x - 3)) + 4)^2 - 5(-2((2x - 3)/(-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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4((-1(-1x^2 + 1x - 3) - 2)/(1(-1x^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": "Find the average of all x-coordinates of local minima of the function f(x) = (-3(-1sin(2\u03c0x + 3) - 3) + 2)/(2(-1sin(2\u03c0x + 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) = (2(2(2cos(3\u03c0(-3|x + 2| - 2)) - 3) - 1) + 2)/(-3(2(2cos(3\u03c0(-3|x + 2| - 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) = -1|(-2((-2x - 1)/(2x + 3))^2 - 5((-2x - 1)/(2x + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(-3cos(1\u03c0x) + 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 x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(-2sin(2\u03c0x + 1))^2 + 4(-2sin(2\u03c0x + 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) = 1(-2|(-1x) - 3|)^2 + 4(-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) = 1sin(2\u03c0(3|((-1x - 3)/(-2x + 3)) + 3| - 2) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3(3(-2cos(1\u03c0x - 1) + 1)^2 + 2(-2cos(1\u03c0x - 1) + 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": "Find the x-coordinate of the local minimum of the function f(x) = 3(4x^2 + 2x) + 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) = -3(1|(-1x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(-2(-3cos(3\u03c0x + 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 extrema (both minima and maxima) does the function f(x) = -3|(2cos(2\u03c0x - 2) - 1) - 3| + 1 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": "Find the x-coordinate of the local minimum of the function f(x) = (-3(-4(-1|x - 1|)^2 + 5) + 2)/(-2(-4(-1|x - 1|)^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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1cos(2\u03c0(-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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3sin(2\u03c0(-2(2|x + 1|) - 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": "How many local maxima does the function f(x) = 2|((3(-1sin(1\u03c0(-2x - 2)) + 2))/(1(-1sin(1\u03c0(-2x - 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": "How many local minima does the function f(x) = -1e^(-1((-3(-1|(1x^2 + 1x - 1) + 3| - 1) + 1)/(-3(-1|(1x^2 + 1x - 1) + 3| - 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 average of all x-coordinates of local maxima of the function f(x) = (2(5(1|(-4x - 1)| - 2)^2 - 1(1|(-4x - 1)| - 2) + 3) - 3)/(-2(5(1|(-4x - 1)| - 2)^2 - 1(1|(-4x - 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 leftmost local minimum of the function f(x) = -5((2(2sin(1\u03c0x) + 3) - 1)/(1(2sin(1\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|((1(4x^2 + 5x - 4) - 1)/(2(4x^2 + 5x - 4) - 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 average of all x-coordinates of local extrema of the function f(x) = 1|(-2cos(2\u03c0x) - 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 average of all x-coordinates of local maxima of the function f(x) = 1|(3sin(3\u03c0(1x^2 + 3x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(-3|(2e^(2((-1x - 3)/(-2x + 1))) - 3) - 1| - 3)^2 - 2(-3|(2e^(2((-1x - 3)/(-2x + 1))) - 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5((-2(-2x^2 + 1x + 5) + 1)/(1(-2x^2 + 1x + 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": "0", "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(-3((1x - 2)/(-3x)) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4(2|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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2(2(-2|x - 2| + 3) + 2)^2 + 2(2(-2|x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(-4x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(-1(-2|((-3x - 3)/(-2x + 1))| + 3) + 3)^2 + 5(-1(-2|((-3x - 3)/(-2x + 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3|(-5(-3cos(1\u03c0(-2x + 2) + 3))^2 + 3(-3cos(1\u03c0(-2x + 2) + 3)) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-3x)^2 + 4(-3x) - 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) = 3(1|(-5((-2x - 1)/(2x + 2)) + 1) + 2|)^2 + 5(1|(-5((-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) = -3e^(2(-2|(-5(-1x^2 + 3x - 2) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1sin(1\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-2(-1sin(1\u03c0x + 2) - 1) - 3)/(-1(-1sin(1\u03c0x + 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 average of all x-coordinates of local extrema of the function f(x) = -1|(-1cos(3\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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(-4(-1((1x + 3)/(2x - 1))^2 + 5((1x + 3)/(2x - 1)) + 3) + 5) + 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 maximum of the function f(x) = -2((3(-1sin(2\u03c0x)))/(3(-1sin(2\u03c0x)) + 2))^2 - 3((3(-1sin(2\u03c0x)))/(3(-1sin(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": "How many local maxima does the function f(x) = 1((-2x + 2)/(1x))^2 + 1((-2x + 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 leftmost local extremum of the function f(x) = 3((1(1|(5x + 4) - 3| + 2) - 3)/(-1(1|(5x + 4) - 3| + 2) - 1))^2 + 5((1(1|(5x + 4) - 3| + 2) - 3)/(-1(1|(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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -4(3(-2|((-1x + 3)/(-2x - 2)) - 3| - 2))^2 - 2(3(-2|((-1x + 3)/(-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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(2|((-2x - 2)/(-2x - 1)) + 3| - 3)^2 - 5(2|((-2x - 2)/(-2x - 1)) + 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 rightmost local maximum of the function f(x) = 2(-1e^(1(2x^2 - 5x + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3((-1(-1(1|x + 2| + 3) + 5) - 2)/(2(-1(1|x + 2| + 3) + 5) - 1))^2 - 3((-1(-1(1|x + 2| + 3) + 5) - 2)/(2(-1(1|x + 2| + 3) + 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 local maximum of the function f(x) = -4((3(3|x - 2| - 3))/(-1(3|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3sin(3\u03c0(2|x| - 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) = (2(2x^2 + 1x - 5) + 1)/(-3(2x^2 + 1x - 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 largest y-value of the function f(x) = -1(-3|((3(2sin(3\u03c0x) - 1) + 3)/(1(2sin(3\u03c0x) - 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": "How many local maxima does the function f(x) = -1|(5(-3((1x - 2)/(-1x))^2 + 4) - 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) = -1(1x^2 - 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 rightmost local maximum of the function f(x) = 2cos(1\u03c0(-3((3x - 1)/(3x + 2))^2 - 2((3x - 1)/(3x + 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": "How many local minima does the function f(x) = 4(3e^(-1(3x^2 + 1x - 5))) + 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 largest y-value of the function f(x) = -1|(-1sin(3\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(3|x + 3| - 1)^2 - 1(3|x + 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(-2x^2 + 3x + 2) - 1)/(2(-2x^2 + 3x + 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 minimum of the function f(x) = (-3(1e^(1(1|(-3x^2 + 2x + 3) + 2| - 2)) + 1) + 3)/(3(1e^(1(1|(-3x^2 + 2x + 3) + 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 extremum with the smallest y-value of the function f(x) = 1cos(2\u03c0(3x - 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) = -5(-2cos(3\u03c0x - 1) - 2)^2 + 5(-2cos(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 x-coordinate of the local extremum of the function f(x) = -1((-3x - 2)/(-1x - 1))^2 + 1((-3x - 2)/(-1x - 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": "How many local maxima does the function f(x) = 4((3(3|x + 1| - 1) - 1)/(1(3|x + 1| - 1)))^2 - 1((3(3|x + 1| - 1) - 1)/(1(3|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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1sin(2\u03c0(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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-3|(3x^2 - 2x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3(1|(-1(-1sin(3\u03c0x + 1) - 1)^2 + 3(-1sin(3\u03c0x + 1) - 1) - 1) - 1| - 2) + 2)/(1(1|(-1(-1sin(3\u03c0x + 1) - 1)^2 + 3(-1sin(3\u03c0x + 1) - 1) - 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 x-coordinate of the rightmost local maximum of the function f(x) = (2(1sin(2\u03c0(-3(-2|x| + 1) - 3) + 1) + 2) + 1)/(-3(1sin(2\u03c0(-3(-2|x| + 1) - 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 local maximum of the function f(x) = -3e^(2(-1((-1(1x - 5) - 1)/(2(1x - 5) + 3))^2 + 2((-1(1x - 5) - 1)/(2(1x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-2(3(-5x^2 + 3x - 2) + 2) - 3)/(1(3(-5x^2 + 3x - 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) = 2(2x^2 + 4x - 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) = -5(2x - 2)^2 - 4(2x - 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 minima does the function f(x) = 3|(4(-2x^2 + 5x + 5) - 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 minimum with the smallest y-value of the function f(x) = -2sin(2\u03c0(4((-2x - 1)/(-1x - 1)) + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3cos(2\u03c0((-1x - 1)/(2x - 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|((2(-3(-1x^2 + 1x - 4) - 4) + 1)/(2(-3(-1x^2 + 1x - 4) - 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 minimum with the smallest y-value of the function f(x) = 1e^(-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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(-1|(3cos(2\u03c0x - 3) - 3) + 3| - 1) - 3)/(-1(-1|(3cos(2\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|(4(2((-1x - 2)/(-2x + 3))^2 + 1((-1x - 2)/(-2x + 3)) - 4) + 4) - 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 extremum of the function f(x) = 2e^(-1(-1|(-1((1x - 1)/(1x - 3)) - 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 extremum of the function f(x) = -2(-1x^2 - 4x + 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 maximum of the function f(x) = (3(-1|(-4x^2 + 5x + 4)| + 1) - 3)/(3(-1|(-4x^2 + 5x + 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 local minimum of the function f(x) = (-3(3(-5(2|x - 3| - 1)^2 + 2) + 2) + 3)/(-2(3(-5(2|x - 3| - 1)^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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|(5((2(4x^2 + 5x + 1) - 3)/(1(4x^2 + 5x + 1) + 2)) - 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": "How many local maxima does the function f(x) = 5(3x + 2)^2 - 4(3x + 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 extrema (both minima and maxima) does the function f(x) = 1(1(1|x + 1|) + 1)^2 - 3(1(1|x + 1|) + 1) - 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 largest y-value of the function f(x) = -2|(-5(3cos(1\u03c0(2x^2 + 2x - 5) + 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 maximum of the function f(x) = -3(1x - 3)^2 + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(1|(-2sin(1\u03c0(5x + 4) - 2) - 2) + 1| + 2) + 3)/(1(1|(-2sin(1\u03c0(5x + 4) - 2) - 2) + 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 extremum of the function f(x) = 1cos(3\u03c0(4x^2 + 4x - 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 minima does the function f(x) = -5((2(-1|(5x + 4)| + 3) - 3)/(3(-1|(5x + 4)| + 3) + 3))^2 - 2((2(-1|(5x + 4)| + 3) - 3)/(3(-1|(5x + 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": "How many local maxima does the function f(x) = -5((3(-5x^2 - 5x) - 3)/(2(-5x^2 - 5x) + 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 maximum with the smallest y-value of the function f(x) = 1|(-2((-2x - 1)/(-3x - 2))^2 + 3((-2x - 1)/(-3x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2(-1|(-3cos(3\u03c0x - 1) + 3) - 3| - 1)^2 + 1(-1|(-3cos(3\u03c0x - 1) + 3) - 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) = 4((3x + 3)/(-2x + 1))^2 + 4((3x + 3)/(-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 maximum with the largest y-value of the function f(x) = (1(4(-1cos(3\u03c0x))^2 + 3(-1cos(3\u03c0x)) - 4) + 2)/(-2(4(-1cos(3\u03c0x))^2 + 3(-1cos(3\u03c0x)) - 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) = 3e^(-1((-3(1|x + 3| - 3) + 1)/(-2(1|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": "-8", "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(-3x^2 - 4x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1e^(-1(-1|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5((-3(-3cos(2\u03c0x - 1) - 2) - 2)/(1(-3cos(2\u03c0x - 1) - 2)))^2 - 2((-3(-3cos(2\u03c0x - 1) - 2) - 2)/(1(-3cos(2\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2(5((-1x + 3)/(2x - 1)) - 5)^2 - 2(5((-1x + 3)/(2x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5((2(3|x| + 1) - 2)/(2(3|x| + 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 extremum of the function f(x) = -3(5(-2|((3x - 2)/(-2x - 1)) - 2| + 3) + 4)^2 - 3(5(-2|((3x - 2)/(-2x - 1)) - 2| + 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": "How many local minima does the function f(x) = 2(2|(2((-1x - 1)/(1x - 3))^2 + 1((-1x - 1)/(1x - 3)) - 1) - 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 of the function f(x) = -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": "How many local minima does the function f(x) = (2(1|(-3(-1x + 5)^2 - 5(-1x + 5) - 3) - 2|))/(2(1|(-3(-1x + 5)^2 - 5(-1x + 5) - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(-2sin(3\u03c0(2|x - 1| - 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 rightmost local extremum of the function f(x) = 4(3sin(2\u03c0x - 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 with the smallest y-value of the function f(x) = 2|((-2(-1(-1x^2 - 4x + 1) - 5) - 2)/(2(-1(-1x^2 - 4x + 1) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2sin(2\u03c0((-1x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 5((-2(2(2e^(-1x) - 1)^2 - 4(2e^(-1x) - 1) + 2) + 3)/(2(2(2e^(-1x) - 1)^2 - 4(2e^(-1x) - 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 extremum of the function f(x) = (-3(-1|(3(-3x^2 - 2) + 3) - 3| + 3))/(3(-1|(3(-3x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(2e^(1(-2|x + 2| + 1)) - 1)^2 + 2(2e^(1(-2|x + 2| + 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) = -5(-2|(-3(-3cos(1\u03c0x) - 1)^2 - 3(-3cos(1\u03c0x) - 1) + 2) - 1| - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1((3(-3|(-5x - 2) + 1|) + 3)/(2(-3|(-5x - 2) + 1|) + 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 average of all x-coordinates of local extrema of the function f(x) = -2|(1sin(3\u03c0((2x + 1)/(-1x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(5(-1e^(-2x) + 2) + 1)^2 + 4(5(-1e^(-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": "How many local minima does the function f(x) = (1(1(-2|(1x^2 - 4) - 3| - 2)) - 1)/(2(1(-2|(1x^2 - 4) - 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": "Find the x-coordinate of the local extremum of the function f(x) = (-2(-2(2x + 5)^2 + 2(2x + 5) + 2))/(-2(-2(2x + 5)^2 + 2(2x + 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"}