{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-4(-2sin(1\u03c0x - 2) + 2)^2 + 5(-2sin(1\u03c0x - 2) + 2) + 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(4(-2x + 3)^2 - 5(-2x + 3) + 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1114", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2((-2(3cos(1\u03c0x + 3) + 3) + 2)/(1(3cos(1\u03c0x + 3) + 3))) - 2)/(3((-2(3cos(1\u03c0x + 3) + 3) + 2)/(1(3cos(1\u03c0x + 3) + 3))) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(-5((3x - 1)/(1x))^2 + 2((3x - 1)/(1x)) + 3) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(4(1|x + 3| - 2)^2 - 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(-1|(2|x - 1| + 1) - 2| + 1) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(1(5x^2 - 3x + 5)^2 + 4(5x^2 - 3x + 5) - 4)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "803", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-2(2|x + 3| - 2)^2 - 4(2|x + 3| - 2)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(-4((1x + 1)/(-3x + 1)) + 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0((-3(1|x + 1| + 3) + 3)/(-1(1|x + 1| + 3) - 1))) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3sin(3\u03c0(1|x + 1| - 3)) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(2cos(1\u03c0((2x - 1)/(1x)) + 2) - 1) - 1)/(2(2cos(1\u03c0((2x - 1)/(1x)) + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(1(3x^2 - 3x - 2)^2 + 5(3x^2 - 3x - 2) + 1) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0((-2(-5x - 2))/(-1(-5x - 2) + 2))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1((3x - 2)/(3x + 2))^2 + 3((3x - 2)/(3x + 2)) + 2) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(1(1x^2 + 2x - 5)^2 + 5) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0((3(-1x^2 + 5x - 4) + 2)/(-3(-1x^2 + 5x - 4) + 4)) - 2) + 3 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": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(4(5x - 4)^2 - 2(5x - 4) + 2) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1450", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(1sin(3\u03c0(1|x + 3| - 1))) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-1|(2x^2 - 4x + 1) - 2| + 3)^2 - 3(-1|(2x^2 - 4x + 1) - 2| + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(3\u03c0(1|((2x - 2)/(-1x + 2)) + 1|) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0((1((-1x + 2)/(1x + 3)) + 1)/(-1((-1x + 2)/(1x + 3)) - 3)) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-4(4x^2 - 1x - 5)^2 - 2(4x^2 - 1x - 5) + 5)^2 + 4(-4(4x^2 - 1x - 5)^2 - 2(4x^2 - 1x - 5) + 5) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(4(-4x^2 - 5x + 5) - 2) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-2(1x^2 + 1x - 3)^2 + 3(1x^2 + 1x - 3) + 1) + 2)/(3(-2(1x^2 + 1x - 3)^2 + 3(1x^2 + 1x - 3) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-2|(2cos(2\u03c0x + 3) - 3) + 2| + 3) - 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(3(-1x^2 - 3x - 3)^2 - 1(-1x^2 - 3x - 3) - 3) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1173", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((-2((-3x - 2)/(-1x - 3)) + 2)/(-2((-3x - 2)/(-1x - 3)) + 3))) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-3(-3cos(1\u03c0x - 1) + 1) - 4) - 1)/(1(-3(-3cos(1\u03c0x - 1) + 1) - 4) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-3cos(1\u03c0(4x^2 + 5x - 1) - 1) + 2)^2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "677", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-3(-5x^2 + 2x + 1)^2 - 3(-5x^2 + 2x + 1) + 1) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-2|(1x^2 - 5x) - 3| + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(-1(2x^2 + 5x - 1) + 4) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-5(3x^2 + 5x - 3)^2 - 2(3x^2 + 5x - 3) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(5((-1x - 1)/(2x + 3)) + 4) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(-4(-3|x + 1| + 3)^2 + 3(-3|x + 1| + 3) + 3) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1131", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(1|(-3sin(2\u03c0x - 3)) + 1| - 2) - 1)/(-2(1|(-3sin(2\u03c0x - 3)) + 1| - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((2(3|x + 2| - 3) + 3)/(-2(3|x + 2| - 3) - 1)) + 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-1|(-4x^2 + 3x + 3) + 1| + 3) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(1\u03c0(3(-1x)^2 - 1(-1x) - 4) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4((3(3sin(3\u03c0x) - 2) - 2)/(3(3sin(3\u03c0x) - 2) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(1(1cos(2\u03c0x - 3) - 3)^2 + 3(1cos(2\u03c0x - 3) - 3) + 2)^2 - 2(1(1cos(2\u03c0x - 3) - 3)^2 + 3(1cos(2\u03c0x - 3) - 3) + 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2(1cos(2\u03c0x + 3) - 2)^2 + 4(1cos(2\u03c0x + 3) - 2) + 3)^2 + 3(-2(1cos(2\u03c0x + 3) - 2)^2 + 4(1cos(2\u03c0x + 3) - 2) + 3) - 5 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 number of x-intercepts of the function f(x) = (-2(-2|(3sin(2\u03c0x + 1)) - 1| + 1) - 1)/(1(-2|(3sin(2\u03c0x + 1)) - 1| + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0(5((2x - 3)/(-1x))^2 - 1((2x - 3)/(-1x)) + 2) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-4(3sin(2\u03c0x + 1) - 1) + 1)^2 - 4(-4(3sin(2\u03c0x + 1) - 1) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3sin(1\u03c0((2x - 2)/(1x - 2)) - 2) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2cos(2\u03c0((3x + 1)/(-1x + 3)) + 3) + 2) + 3)/(-2(-2cos(2\u03c0((3x + 1)/(-1x + 3)) + 3) + 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(2\u03c0(2|((-1x - 3)/(-2x - 2)) + 3| + 2) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2(-1x^2 + 2x + 5)^2 + 2(-1x^2 + 2x + 5) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-4(-1|x - 3| + 2) + 3) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3sin(1\u03c0((-1x + 2)/(1x)) - 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(3(1x^2 + 2x + 3) + 3) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(-1|x + 2| + 2) + 2)^2 + 4(5(-1|x + 2| + 2) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(2cos(3\u03c0((1x - 2)/(1x)) + 2)) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2cos(3\u03c0(-4x - 2) - 1) - 2) + 1)/(-3(2cos(3\u03c0(-4x - 2) - 1) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-2cos(1\u03c0((2x - 3)/(-3x - 2)) + 1) - 2) + 2)/(-2(-2cos(1\u03c0((2x - 3)/(-3x - 2)) + 1) - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2(3|x - 3| - 2)^2 + 1(3|x - 3| - 2) - 4) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(2cos(1\u03c0(2|x + 1| + 1) + 3)) - 5 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": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(1|(-3|x - 3|) + 1| + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(2cos(3\u03c0(-1x + 5) + 2) - 2) - 3)/(2(2cos(3\u03c0(-1x + 5) + 2) - 2) - 1) 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 number of x-intercepts of the function f(x) = 1cos(2\u03c0(-1(3|x + 1| + 3)^2 - 4) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1275", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(2sin(3\u03c0(-2|x - 1| - 1) - 3) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(-1|(-1x^2 + 4x + 4) - 3| - 3) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-1(-2cos(2\u03c0x - 2) - 2)^2 - 1(-2cos(2\u03c0x - 2) - 2) + 2) - 3)/(1(-1(-2cos(2\u03c0x - 2) - 2)^2 - 1(-2cos(2\u03c0x - 2) - 2) + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0(1(2|x + 3| - 2) - 3) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0((-1(-1x^2 - 5x) - 3)/(-3(-1x^2 - 5x) - 1)) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(3sin(3\u03c0(1x^2 - 4x - 1) + 2) + 1)^2 - 2(3sin(3\u03c0(1x^2 - 4x - 1) + 2) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1096", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-1(-3sin(2\u03c0x + 3) - 3) + 1) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(4(-3x^2 - 3x + 4)^2 + 4(-3x^2 - 3x + 4) - 4) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2|(-2sin(3\u03c0x + 1) + 2)| - 3)^2 - 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": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-1|((2x)/(3x + 3)) + 1| + 2)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(2(-5x^2 - 2x - 5)^2 - 5(-5x^2 - 2x - 5)) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "849", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-1((-1x + 2)/(-1x + 3))^2 - 1((-1x + 2)/(-1x + 3)) + 5) - 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-1|(2cos(3\u03c0x + 1) + 1)| + 2) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-2sin(1\u03c0(-2|x + 2| + 2) + 2) - 3) + 1)/(-2(-2sin(1\u03c0(-2|x + 2| + 2) + 2) - 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(2\u03c0(-2(2x^2 - 2x + 4)^2 - 1(2x^2 - 2x + 4) + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1494", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-2|(-2sin(3\u03c0x) - 1) + 3| - 3) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(2sin(1\u03c0(-4x - 1)) - 1))/(-3(2sin(1\u03c0(-4x - 1)) - 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-3cos(2\u03c0(1x^2 + 2x - 5) + 2) - 1)^2 + 5(-3cos(2\u03c0(1x^2 + 2x - 5) + 2) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "751", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3sin(3\u03c0(-5x^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": "1643", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2sin(2\u03c0((3x + 2)/(2x + 2)) + 1) - 2)^2 - 4(-2sin(2\u03c0((3x + 2)/(2x + 2)) + 1) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((2(-3cos(2\u03c0x - 2) - 2) - 1)/(-1(-3cos(2\u03c0x - 2) - 2) - 1))^2 - 2((2(-3cos(2\u03c0x - 2) - 2) - 1)/(-1(-3cos(2\u03c0x - 2) - 2) - 1)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-2(-1sin(3\u03c0x + 1) + 1) - 3)/(2(-1sin(3\u03c0x + 1) + 1) - 1))^2 - 4((-2(-1sin(3\u03c0x + 1) + 1) - 3)/(2(-1sin(3\u03c0x + 1) + 1) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1sin(2\u03c0(4x - 2)))| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(2cos(3\u03c0(3x^2 - 5x + 5) - 3) + 3) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1434", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(4(-1x^2 + 5x - 1) - 4)^2 + 2(4(-1x^2 + 5x - 1) - 4) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(3(-2e^(1x) + 2)^2 - 3(-2e^(1x) + 2) - 3) + 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(3\u03c0(5((3x + 3)/(1x))^2 + 3((3x + 3)/(1x)) - 4) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0((-1(5x + 1) + 3)/(-1(5x + 1) - 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(5(2e^(-2x) - 3)^2 - 4)^2 + 5(5(2e^(-2x) - 3)^2 - 4) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-2(4x^2 - 4x + 5) + 1) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1091", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(1\u03c0(5(1|x - 3| + 1)^2 + 1(1|x - 3| + 1) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1226", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(3sin(3\u03c0(4x^2 + 3x - 5) + 2))^2 + 1(3sin(3\u03c0(4x^2 + 3x - 5) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(1cos(3\u03c0(3|x + 3| - 1)) - 1) - 3)/(2(1cos(3\u03c0(3|x + 3| - 1)) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3e^(1(-3(-1x^2 + 5x - 5)^2 - 4(-1x^2 + 5x - 5) - 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(3cos(2\u03c0(2|x - 2| - 2)) - 1) - 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(2\u03c0(-4((2x + 2)/(3x - 1))^2 + 3((2x + 2)/(3x - 1)) - 3) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(5(-2sin(1\u03c0x - 3) - 3) + 5) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(3|(5x^2 + 3x + 2) - 2|)| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-1sin(1\u03c0(-3|x - 2|) - 2) + 2)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(2|(-5x^2 - 2x + 2) - 3| - 3) - 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3cos(2\u03c0(5x + 3) - 2) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-3|(5x^2 - 4) - 1| + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(1|(-1|x + 3| - 3) - 2| + 3) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0((-2(-5x^2 - 2x + 5))/(3(-5x^2 - 2x + 5) + 2)) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-3(-1|x - 1| + 1)^2 + 3) - 2)/(-2(-3(-1|x - 1| + 1)^2 + 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-4(1|x| - 1) + 1)^2 + 1(-4(1|x| - 1) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) + 1) - 1)/(-2(-4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) + 1) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(-1|(1|x - 3| + 3)| - 3) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(3(-3cos(2\u03c0x - 2) + 2) - 2)^2 + 3(3(-3cos(2\u03c0x - 2) + 2) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-4(-2sin(2\u03c0x + 1) + 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(2cos(2\u03c0((1x + 2)/(3x))) + 1) + 1)/(1(2cos(2\u03c0((1x + 2)/(3x))) + 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-2cos(3\u03c0(-2|x - 1| + 1)) + 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2(2x^2 - 5x - 3)^2 + 4(2x^2 - 5x - 3) - 2) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(-3((-3x + 2)/(-1x - 3)) - 5) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(1(-3cos(1\u03c0x + 3) - 1)^2 + 1(-3cos(1\u03c0x + 3) - 1) - 4))/(3(1(-3cos(1\u03c0x + 3) - 1)^2 + 1(-3cos(1\u03c0x + 3) - 1) - 4) + 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": "How many solutions does the equation 4(3sin(2\u03c0(1|x| + 1) - 1) + 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(2cos(1\u03c0(-2x + 4) - 1) - 1) + 3)/(2(2cos(1\u03c0(-2x + 4) - 1) - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1(3sin(2\u03c0x - 3) - 2)^2 - 5(3sin(2\u03c0x - 3) - 2)) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(2cos(3\u03c0(-2x^2 + 2) - 1) + 3) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3sin(1\u03c0((2x + 2)/(3x + 1)) - 1) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-3sin(1\u03c0((-3x + 1)/(1x + 1)) + 1) - 1) - 1)/(-1(-3sin(1\u03c0((-3x + 1)/(1x + 1)) + 1) - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(2(1|x + 1| + 1) - 5)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(1|(2|x + 2| + 2) - 1| + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3|(-1x^2 + 4x + 1)| + 1)^2 - 3(3|(-1x^2 + 4x + 1)| + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(3cos(3\u03c0(5x^2 + 5x + 3) - 1) + 1) - 1)/(1(3cos(3\u03c0(5x^2 + 5x + 3) - 1) + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1514", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(2|(-2x + 4) - 3| - 1)^2 + 5(2|(-2x + 4) - 3| - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(-4(-4x + 3) + 5) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(-3|x - 2|) + 2| + 2)^2 + 4(-1|(-3|x - 2|) + 2| + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-5((-1x + 2)/(-1x))^2 + 5((-1x + 2)/(-1x)) + 5)^2 + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-1(3sin(3\u03c0x + 2))^2 + 5(3sin(3\u03c0x + 2)) + 4) - 2)/(-1(-1(3sin(3\u03c0x + 2))^2 + 5(3sin(3\u03c0x + 2)) + 4) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0(-4((3x - 2)/(-3x))^2 - 5((3x - 2)/(-3x)) - 5) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(3sin(3\u03c0(4x) + 1) - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(1(-1sin(1\u03c0x) - 1)^2 - 5(-1sin(1\u03c0x) - 1) - 4) - 3)/(1(1(-1sin(1\u03c0x) - 1)^2 - 5(-1sin(1\u03c0x) - 1) - 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2cos(2\u03c0(-4x - 2) + 1) + 1))/(-2(2cos(2\u03c0(-4x - 2) + 1) + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2sin(2\u03c0(-4x - 2) + 3) - 2) - 3)/(2(2sin(2\u03c0(-4x - 2) + 3) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(3sin(2\u03c0(-1x^2 - 3x - 4))) + 3)/(-1(3sin(2\u03c0(-1x^2 - 3x - 4))) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "410", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(3cos(2\u03c0((3x + 2)/(-1x + 3)) + 2)) + 2)/(-3(3cos(2\u03c0((3x + 2)/(-1x + 3)) + 2)) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3(5x^2 + 3x - 4)^2 - 2(5x^2 + 3x - 4) - 3) - 2)/(1(3(5x^2 + 3x - 4)^2 - 2(5x^2 + 3x - 4) - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(1(3|x - 1| + 2)^2 + 4(3|x - 1| + 2)) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1441", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-3(3sin(1\u03c0x) - 1) - 5) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0(-3|(2x^2 + 3x) - 1| + 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(5((1x)/(3x - 1))^2 + 5((1x)/(3x - 1)) + 2) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((2(-3x^2 + 2) - 2)/(-1(-3x^2 + 2) - 2)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-3cos(3\u03c0(-2x - 4) + 1) + 1))/(-3(-3cos(3\u03c0(-2x - 4) + 1) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-2cos(3\u03c0(-4x^2 - 4x + 4) - 2) - 2) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1478", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-4(1x + 4) - 3) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(3\u03c0(1(2|x + 2|) - 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": "Determine the number of values x in [-10, 10] where f(x) = 1(-1(-3x^2 - 5x + 3)^2 + 2(-3x^2 - 5x + 3) + 5)^2 + 4(-1(-3x^2 - 5x + 3)^2 + 2(-3x^2 - 5x + 3) + 5) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0(2|((1x + 3)/(-1x)) - 1| - 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-1(3x^2 - 2x) - 2)/(-2(3x^2 - 2x) + 3)) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(3sin(3\u03c0((1x + 2)/(3x + 1)) - 1)) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(-3|(1|x - 3| - 1) - 2| + 1) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-4(1x^2 - 1x - 1)^2 - 2(1x^2 - 1x - 1) - 1)^2 - 3(-4(1x^2 - 1x - 1)^2 - 2(1x^2 - 1x - 1) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0(-1(-3x - 5) - 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(-2|(-3|x| - 1) - 2|) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(-1((3x)/(2x - 3))^2 - 1((3x)/(2x - 3)) + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2|(-4x^2 + 2x + 5) - 2| - 1)^2 + 5(2|(-4x^2 + 2x + 5) - 2| - 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-2(-1x^2 + 3) + 2)| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(1cos(2\u03c0(2|x + 3| - 3)) + 2) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(1sin(3\u03c0(2x - 1) - 3))^2 + 4(1sin(3\u03c0(2x - 1) - 3)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(4((2x + 3)/(3x + 2))^2 + 5((2x + 3)/(3x + 2)) - 3)^2 + 3(4((2x + 3)/(3x + 2))^2 + 5((2x + 3)/(3x + 2)) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-4(-3sin(1\u03c0x + 1) - 1)^2 - 5(-3sin(1\u03c0x + 1) - 1) + 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(2sin(1\u03c0(-1x + 4) + 3) + 2)^2 - 2(2sin(1\u03c0(-1x + 4) + 3) + 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(2(3sin(3\u03c0x - 2) - 2)^2 - 5)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(2(-3sin(2\u03c0x + 1) + 1)^2 - 3(-3sin(2\u03c0x + 1) + 1) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(2|(1x - 4) - 2| - 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-5(1sin(2\u03c0x - 1) - 1)^2 + 3(1sin(2\u03c0x - 1) - 1) + 4)^2 + 5(-5(1sin(2\u03c0x - 1) - 1)^2 + 3(1sin(2\u03c0x - 1) - 1) + 4) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|((-2(-2|x + 3| + 2) + 2)/(-2(-2|x + 3| + 2))) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-1sin(3\u03c0((-2x - 1)/(2x - 1)) - 2) - 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-2cos(1\u03c0(1|x - 3| + 1) - 2) - 2)^2 - 2(-2cos(1\u03c0(1|x - 3| + 1) - 2) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-5(5x - 2)^2 + 4(5x - 2) + 4)^2 + 3(-5(5x - 2)^2 + 4(5x - 2) + 4) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(3cos(3\u03c0(-3x^2 + 3x + 1) + 3) + 1)| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1113", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(2\u03c0(-1(-1|x| - 2) + 1) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-3(1sin(2\u03c0x - 2) + 1))/(1(1sin(2\u03c0x - 2) + 1) + 1))| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(-2(-1|x + 3| + 1)^2 - 2) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(2(-1x - 5) + 5) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(1sin(1\u03c0(5x^2 - 1x - 3) - 2) + 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "436", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(1\u03c0(-2((-3x - 3)/(-1x + 3))^2 + 5((-3x - 3)/(-1x + 3)) + 5) - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "281", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(2sin(1\u03c0((3x - 1)/(-1x + 2)) + 1) - 2)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(3|(-1x^2 - 2x + 1) + 2| + 1) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(4(-2|x + 3|)^2 - 3(-2|x + 3|) - 2)| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2sin(1\u03c0(3x - 1) - 1)) + 2)/(2(2sin(1\u03c0(3x - 1) - 1)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(1sin(2\u03c0(-1x + 5) - 2)))/(2(1sin(2\u03c0(-1x + 5) - 2)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(-3(-4x^2 + 1x - 5)) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(2\u03c0(3x^2 + 2x) + 3) - 2) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1145", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3(1x^2 + 1x - 4)^2 - 1(1x^2 + 1x - 4) - 1) - 2)/(2(3(1x^2 + 1x - 4)^2 - 1(1x^2 + 1x - 4) - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(2|(-5x^2 - 4x + 3) + 1| + 1) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0(3|(-2|x| + 1) - 1| + 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(1(-1|x - 1| - 2)^2 + 5(-1|x - 1| - 2) - 5) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(-2|(-1|x - 3| + 3) + 2| + 1) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(1|(-1x^2 - 5x + 5) - 2| - 2)^2 - 3(1|(-1x^2 - 5x + 5) - 2| - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0((1((3x + 2)/(-3x + 2)) - 2)/(2((3x + 2)/(-3x + 2)) + 2)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((2(-2cos(2\u03c0x - 3) - 1) - 2)/(3(-2cos(2\u03c0x - 3) - 1) + 1)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(5(-2|x + 3| + 2)^2 + 4(-2|x + 3| + 2) + 1)^2 - 1(5(-2|x + 3| + 2)^2 + 4(-2|x + 3| + 2) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-4(1x^2 - 5) + 1)^2 - 2(-4(1x^2 - 5) + 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2|(-3|x + 2| + 3) + 1| - 2)^2 + 1(2|(-3|x + 2| + 3) + 1| - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2|(3x^2 - 1x - 4) + 2| - 2)^2 - 5(2|(3x^2 - 1x - 4) + 2| - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-1(-2sin(2\u03c0x) - 1) + 2) + 3)/(-1(-1(-2sin(2\u03c0x) - 1) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-2sin(3\u03c0(3|x + 1| + 2) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-2((1x + 2)/(2x - 1))) + 1) 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": "How many solutions does the equation (-1(4(-2sin(2\u03c0x) - 1) - 4) - 1)/(1(4(-2sin(2\u03c0x) - 1) - 4)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(-1|(3x^2 - 1x + 3) + 1|) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1444", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0((1((1x + 2)/(-3x + 4)))/(1((1x + 2)/(-3x + 4)) + 2)) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((2(-2cos(1\u03c0x - 3) + 1) - 1)/(2(-2cos(1\u03c0x - 3) + 1) + 1)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1|(2|x - 1|) - 1|)^2 + 3(1|(2|x - 1|) - 1|) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1(-2sin(1\u03c0x - 3) - 1) - 1) - 3| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(-3((-3x + 2)/(-3x + 1))^2 + 3((-3x + 2)/(-3x + 1)) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(3|(-4x^2 + 4) - 3| - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0((2(2|x| - 3) - 3)/(2(2|x| - 3) - 1)) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(-1x + 5)^2 + 4(-1x + 5) + 5) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(1(1x^2 - 3x + 4)^2 - 4(1x^2 - 3x + 4) - 2) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1212", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(4(-1|x - 1| - 3) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(2|((3x + 2)/(1x)) + 2| - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-2|(3|x| + 1) - 2| - 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(3|(-5x + 3) - 1| - 2)^2 + 5(3|(-5x + 3) - 1| - 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(-5(5x + 4)^2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1507", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-1sin(3\u03c0((-3x - 3)/(-2x + 3)) + 3) + 2) - 1)/(-1(-1sin(3\u03c0((-3x - 3)/(-2x + 3)) + 3) + 2) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(2|(5x - 5) - 1| + 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-1(-2sin(1\u03c0x - 3)) + 1)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|((2(-4x^2 + 3) - 1)/(2(-4x^2 + 3)))| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(1(1|x + 2| + 3) - 5) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(3|((2x - 1)/(-1x - 1)) + 1|) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1(-2cos(1\u03c0x - 3) - 2)^2 - 5(-2cos(1\u03c0x - 3) - 2) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3(1x^2 - 1x - 3) + 4)^2 - 4(-3(1x^2 - 1x - 3) + 4) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(5(-5x + 2) + 3) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1(-1x^2 + 5x) + 4) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2((3(-3sin(2\u03c0x - 1) + 2) - 3)/(-3(-3sin(2\u03c0x - 1) + 2) - 1)) - 1)/(-1((3(-3sin(2\u03c0x - 1) + 2) - 3)/(-3(-3sin(2\u03c0x - 1) + 2) - 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1(1x^2 + 1x - 4)^2 - 1(1x^2 + 1x - 4) + 4)^2 - 3(-1(1x^2 + 1x - 4)^2 - 1(1x^2 + 1x - 4) + 4) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(-5((2x - 3)/(2x + 3)) - 4) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(5(-3x - 3) - 2) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "423", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(1sin(1\u03c0(2x + 5) + 3) + 3) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(3|(1x^2 + 4x + 3) + 3| - 1) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "769", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1|(1sin(2\u03c0x - 1) + 1) - 3| - 2) - 3)/(2(1|(1sin(2\u03c0x - 1) + 1) - 3| - 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-4(1cos(1\u03c0x - 3))^2 + 4(1cos(1\u03c0x - 3)))^2 + 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 number of x-intercepts of the function f(x) = 1sin(3\u03c0(-3|((-2x)/(-2x - 1)) + 1| - 1) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((2(3sin(2\u03c0x + 3) - 2) - 3)/(-2(3sin(2\u03c0x + 3) - 2)))^2 + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(3sin(2\u03c0(-3x^2 + 5x + 3) + 1) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1066", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(-4(-5x - 3)^2 - 3(-5x - 3) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1575", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(3\u03c0(2(5x + 5)^2 + 1(5x + 5)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1227", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2|(-1|x - 3| - 2) + 3| + 3)^2 + 1(-2|(-1|x - 3| - 2) + 3| + 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(2\u03c0(5(2|x|) + 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(5(2|x + 1| - 2)^2 + 1(2|x + 1| - 2) - 4) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1015", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-1|(-5x - 1) + 1| + 2) + 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3cos(3\u03c0(-3x^2 + 3x + 1) - 2) - 1) - 2)/(-1(3cos(3\u03c0(-3x^2 + 3x + 1) - 2) - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "856", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(3(-4x^2 - 2x + 1)^2 - 1(-4x^2 - 2x + 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(-4(-3x^2 - 2x + 2)^2 - 5(-3x^2 - 2x + 2) + 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1096", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-2((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)))^2 + 4(-2((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2))) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1((1(1cos(3\u03c0x - 1) - 1) + 3)/(1(1cos(3\u03c0x - 1) - 1) + 1)) + 2)/(2((1(1cos(3\u03c0x - 1) - 1) + 3)/(1(1cos(3\u03c0x - 1) - 1) + 1)) - 1) 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": "Determine the number of values x in [-10, 10] where f(x) = (-1((1(1cos(3\u03c0x - 3) + 1) - 2)/(-3(1cos(3\u03c0x - 3) + 1) + 4)) + 3)/(1((1(1cos(3\u03c0x - 3) + 1) - 2)/(-3(1cos(3\u03c0x - 3) + 1) + 4)) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2|(1x - 5) - 2| - 1)^2 + 5(2|(1x - 5) - 2| - 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(3sin(1\u03c0(4x^2 - 3x - 3) - 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "798", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(4(3|x + 2| + 2) - 5) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0(2|(2x - 4) + 2| - 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(2(-1x - 1) - 1) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-2|((3x + 2)/(2x + 3)) + 3| + 3)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((-3(-2|x - 3| + 1))/(1(-2|x - 3| + 1) + 1))^2 + 4((-3(-2|x - 3| + 1))/(1(-2|x - 3| + 1) + 1)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(-3(-4x - 2)^2 + 5(-4x - 2) + 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1570", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-2(3x^2 + 5x + 1)^2 + 2(3x^2 + 5x + 1) + 5) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(2|((1x - 3)/(-3x + 4)) + 1| - 3) - 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2cos(3\u03c0(-3x + 4) + 3) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(3((1x - 1)/(-1x + 2))^2 + 3((1x - 1)/(-1x + 2)) - 2) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0((1(-1x - 4) - 1)/(2(-1x - 4) + 2)) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(2(2x^2 + 2x - 1)^2 - 3(2x^2 + 2x - 1) - 3) - 3)/(1(2(2x^2 + 2x - 1)^2 - 3(2x^2 + 2x - 1) - 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(3cos(3\u03c0(-1|x - 3|) + 3) - 3)| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-2|(2cos(2\u03c0x - 1) + 2) - 1| + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3cos(3\u03c0(-2x - 1) - 2) + 2) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-2cos(2\u03c0(-2|x| - 3) - 2) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(2(1x^2 + 4x - 1)^2 + 5(1x^2 + 4x - 1) - 3)^2 + 3(2(1x^2 + 4x - 1)^2 + 5(1x^2 + 4x - 1) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3(-1|x + 1| + 2)^2 + 3(-1|x + 1| + 2) - 1)^2 + 2(3(-1|x + 1| + 2)^2 + 3(-1|x + 1| + 2) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-2cos(1\u03c0((-2x + 3)/(-3x + 4)) - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(1(-1sin(2\u03c0x - 3) - 1) + 1) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(2cos(2\u03c0((-1x + 3)/(-2x + 1)) + 1)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0(1(1|x - 2| - 1) - 2) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(5((-2x + 3)/(1x + 3))^2 - 5((-2x + 3)/(1x + 3)) - 1) + 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0(1(3x^2 - 1x - 3)^2 + 2(3x^2 - 1x - 3) + 1) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1146", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-4(2|x + 1| - 3)^2 - 1(2|x + 1| - 3) + 3)^2 - 1(-4(2|x + 1| - 3)^2 - 1(2|x + 1| - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0((-1(2x^2 - 3x - 2) + 2)/(2(2x^2 - 3x - 2) + 1)) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0(4(1|x - 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": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(1cos(3\u03c0(-4x + 5)) + 2) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2((-1(3sin(2\u03c0x - 2) + 2) + 1)/(-1(3sin(2\u03c0x - 2) + 2))))/(-3((-1(3sin(2\u03c0x - 2) + 2) + 1)/(-1(3sin(2\u03c0x - 2) + 2))) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(3(3|x + 3| - 2) - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3\u03c0(-5((2x + 3)/(-2x - 2))^2 - 1((2x + 3)/(-2x - 2)) - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2|((1x - 1)/(-3x + 2)) + 1| + 3)^2 + 3(-2|((1x - 1)/(-3x + 2)) + 1| + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-1(-5x^2 + 4x + 4)^2 - 3(-5x^2 + 4x + 4) - 2) + 1)/(-1(-1(-5x^2 + 4x + 4)^2 - 3(-5x^2 + 4x + 4) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0((-1(3x^2 - 4x - 1) - 3)/(-1(3x^2 - 4x - 1) + 2)) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(4(3|x - 3| + 2) - 4) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2|(-2sin(3\u03c0x - 1) + 2) - 2|) + 1)/(-1(2|(-2sin(3\u03c0x - 1) + 2) - 2|) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-1sin(1\u03c0(-3|x - 1| + 3) + 1) - 3)^2 + 2(-1sin(1\u03c0(-3|x - 1| + 3) + 1) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(1sin(2\u03c0(-4x^2 - 4x - 2) + 2) - 2)^2 + 4(1sin(2\u03c0(-4x^2 - 4x - 2) + 2) - 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2cos(3\u03c0((-1x + 1)/(-3x - 2)) - 2) - 1)^2 + 2(-2cos(3\u03c0((-1x + 1)/(-3x - 2)) - 2) - 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(1|(-5x^2 - 2x + 1) - 2| - 2)^2 + 5(1|(-5x^2 - 2x + 1) - 2| - 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2cos(2\u03c0(3x^2 - 3x - 3) - 3) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1022", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-3cos(3\u03c0(2x^2 + 1x + 1) + 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1129", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(3sin(3\u03c0(-3x^2 + 1x + 5) - 1) + 1) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "753", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0((3((-1x + 2)/(-3x + 1)) + 3)/(-2((-1x + 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": "49", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1|(2|x + 3| - 1) - 3| + 1)^2 + 3(-1|(2|x + 3| - 1) - 3| + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(3|(4x^2 + 3x - 2) - 3| + 2)^2 + 4(3|(4x^2 + 3x - 2) - 3| + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1cos(3\u03c0(5x - 1) + 3) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3sin(1\u03c0(-5x^2 - 5x + 4) - 1) - 3)^2 + 2(-3sin(1\u03c0(-5x^2 - 5x + 4) - 1) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "761", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(2sin(2\u03c0(5x^2 - 2x + 1) - 3) - 1) - 1)/(3(2sin(2\u03c0(5x^2 - 2x + 1) - 3) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(2cos(2\u03c0(2|x + 2| + 2)) - 3) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3cos(1\u03c0(3x + 5) - 3) - 3) - 1)/(-3(-3cos(1\u03c0(3x + 5) - 3) - 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2|(-3sin(2\u03c0x - 1) + 2) - 2| + 1)^2 + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(2|(5x) - 1| - 2) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2((2(2|x - 2| - 1) + 1)/(3(2|x - 2| - 1) + 3))^2 - 3((2(2|x - 2| - 1) + 1)/(3(2|x - 2| - 1) + 3)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(5(-1cos(2\u03c0x + 1)) + 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-1(-2x^2 + 4x + 5) + 5)| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3((1(-2x^2 - 2x + 4) + 1)/(3(-2x^2 - 2x + 4) - 1))^2 - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(2\u03c0(1(-2x^2 + 5x - 1)^2 + 4(-2x^2 + 5x - 1) + 4)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(2|(1|x - 3| + 2)| - 2) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(2cos(1\u03c0(-2x - 4) - 3) + 1) + 1)/(-3(2cos(1\u03c0(-2x - 4) - 3) + 1) - 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 number of x-intercepts of the function f(x) = -5(-3(2cos(1\u03c0x - 2) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(3\u03c0(-2(4x^2 - 1x + 2) + 2) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1071", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-3(-3x^2 + 3x + 2) - 5)^2 - 4(-3(-3x^2 + 3x + 2) - 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2cos(2\u03c0(-1|x|) - 3) + 1) - 1)/(3(2cos(2\u03c0(-1|x|) - 3) + 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(3(-1x - 1)^2 - 3(-1x - 1) - 5) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "603", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-1|((-1x + 2)/(-2x - 2)) - 2|) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2(-2x^2 - 3x + 4)^2 + 5(-2x^2 - 3x + 4) - 4) - 1)/(-3(2(-2x^2 - 3x + 4)^2 + 5(-2x^2 - 3x + 4) - 4)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(3sin(2\u03c0(-5x^2 - 3x - 1) + 2) + 2) + 2)/(-1(3sin(2\u03c0(-5x^2 - 3x - 1) + 2) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1cos(3\u03c0(-3|x + 2| - 2)) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1(2sin(2\u03c0x + 3) + 1)^2 - 5(2sin(2\u03c0x + 3) + 1) - 4) - 2)/(-2(1(2sin(2\u03c0x + 3) + 1)^2 - 5(2sin(2\u03c0x + 3) + 1) - 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2cos(1\u03c0(2x^2 - 1x - 1) + 3) - 2)^2 + 4(2cos(1\u03c0(2x^2 - 1x - 1) + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((3(-3cos(3\u03c0x + 3) - 3) + 3)/(2(-3cos(3\u03c0x + 3) - 3) - 1)) - 1)/(1((3(-3cos(3\u03c0x + 3) - 3) + 3)/(2(-3cos(3\u03c0x + 3) - 3) - 1)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(-4(-1x^2 + 3x + 3)^2 + 3(-1x^2 + 3x + 3) + 4) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1333", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(-5((-2x + 2)/(-1x - 1))^2 - 3((-2x + 2)/(-1x - 1)) - 4) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(2(4x - 2)^2 + 3(4x - 2) - 2) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1526", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3sin(3\u03c0(-2|x + 2| + 2) - 3) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-5(-1|x + 3| + 3)^2 + 2(-1|x + 3| + 3) + 3) - 2)/(-2(-5(-1|x + 3| + 3)^2 + 2(-1|x + 3| + 3) + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3|(-3|x + 3| + 1) + 2| - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0((-2(-2|x - 2|) + 1)/(-2(-2|x - 2|) - 3)) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4((1(-1cos(3\u03c0x + 1) + 2) - 2)/(2(-1cos(3\u03c0x + 1) + 2) - 1))^2 + 2((1(-1cos(3\u03c0x + 1) + 2) - 2)/(2(-1cos(3\u03c0x + 1) + 2) - 1)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-1sin(2\u03c0(-1x - 1) + 1) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3e^(-1(5(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 3) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3((-2(3x^2 - 4x - 3) + 3)/(3(3x^2 - 4x - 3) - 1))^2 + 4((-2(3x^2 - 4x - 3) + 3)/(3(3x^2 - 4x - 3) - 1)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(1\u03c0((3(3|x + 3| - 3))/(-1(3|x + 3| - 3) + 3)) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1sin(3\u03c0(2|x - 2| - 1) + 2) - 2) - 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": "How many zeros does the function f(x) = 3cos(1\u03c0((-1(1x + 5) - 2)/(-3(1x + 5))) + 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 zeros does the function f(x) = -3sin(2\u03c0(-5(3|x + 3| + 3) + 4) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(3\u03c0(-3|(-1|x + 1| - 1) - 3|) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1cos(3\u03c0(-3|x - 2|) + 3) - 2) + 3)/(1(-1cos(3\u03c0(-3|x - 2|) + 3) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3\u03c0((-2((3x - 2)/(3x)))/(1((3x - 2)/(3x)) + 2))) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-2cos(2\u03c0((2x)/(-2x + 3)) + 1) + 2) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-3(1|x + 1|)^2 - 5(1|x + 1|) + 2)^2 + 1(-3(1|x + 1|)^2 - 5(1|x + 1|) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-3sin(2\u03c0(-3|x - 1| - 2) - 3) - 2))/(-2(-3sin(2\u03c0(-3|x - 1| - 2) - 3) - 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-4(-2cos(1\u03c0x - 2))^2 + 5(-2cos(1\u03c0x - 2)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(5(-3cos(1\u03c0x) - 2)^2 - 1(-3cos(1\u03c0x) - 2) - 4) + 1)/(-3(5(-3cos(1\u03c0x) - 2)^2 - 1(-3cos(1\u03c0x) - 2) - 4) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(-3x - 4)^2 - 3(-3x - 4) + 5)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-5(2x + 2)^2 + 1(2x + 2) + 2)^2 + 1(-5(2x + 2)^2 + 1(2x + 2) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(5(1|x + 2| - 3)^2 - 3(1|x + 2| - 3) - 3) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1218", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3sin(3\u03c0(1x + 2) - 3) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-3(3cos(3\u03c0x + 3) - 3) - 3) + 3)/(-1(-3(3cos(3\u03c0x + 3) - 3) - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3(1e^(1x) - 2)^2 + 4)^2 - 3(-3(1e^(1x) - 2)^2 + 4) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(3|(4x^2 - 2x - 1) + 3| - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1632", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-2|(-3cos(2\u03c0x + 3) - 1) + 3| - 2) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(3|(5x^2 - 4x) + 1| - 3) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1457", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(3(-1cos(2\u03c0x + 2) - 1) + 5) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(2cos(1\u03c0((-2x)/(3x + 2)) + 1) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-2sin(3\u03c0(-3x) - 2) - 2) - 3)/(-1(-2sin(3\u03c0(-3x) - 2) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3(-1x^2 + 5))^2 - 2(3(-1x^2 + 5)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(5((-1x - 1)/(-2x)) - 4) + 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(4(-3x - 2)^2 - 4(-3x - 2) - 5) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1485", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-3(-3x^2 - 4x - 2)^2 - 4(-3x^2 - 4x - 2) + 5)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1334", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1cos(1\u03c0(1x + 1) + 1) - 3) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-3sin(3\u03c0(-3|x + 3| - 1) + 2)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(1(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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-5(-5x^2 - 3x + 2) + 1)^2 + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2(2sin(3\u03c0x + 3) + 2)) - 1 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": "Determine the number of values x in [-10, 10] where f(x) = -5(-3(1cos(1\u03c0x + 3))^2 - 4(1cos(1\u03c0x + 3)) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-1|(2cos(3\u03c0x) + 1)| - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-2sin(3\u03c0(1|x + 2| + 3) + 3)) - 3)/(-3(-2sin(3\u03c0(1|x + 2| + 3) + 3)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(2cos(3\u03c0(3|x - 1| - 1) + 3)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2cos(3\u03c0((-2x + 2)/(2x + 1)) + 1) - 1) + 1)/(-3(2cos(3\u03c0((-2x + 2)/(2x + 1)) + 1) - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5((2(1cos(3\u03c0x + 3)) + 2)/(-3(1cos(3\u03c0x + 3)) - 1)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2((2(-3sin(1\u03c0x - 2)))/(-3(-3sin(1\u03c0x - 2)) - 1)) - 2)/(-3((2(-3sin(1\u03c0x - 2)))/(-3(-3sin(1\u03c0x - 2)) - 1)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3cos(2\u03c0(-3x^2 - 1)) - 2) - 3)/(1(3cos(2\u03c0(-3x^2 - 1)) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1132", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(4(3sin(1\u03c0x - 1) + 1)^2 - 1(3sin(1\u03c0x - 1) + 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|((-2(3sin(2\u03c0x) + 3) + 3)/(2(3sin(2\u03c0x) + 3) - 1))| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(1(-1x^2 - 3x + 2) + 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3cos(1\u03c0(1x - 5) - 2) - 1) - 3)/(-3(-3cos(1\u03c0(1x - 5) - 2) - 1) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-4(5x - 3)^2 + 2(5x - 3)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1423", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(-2|(-3|x| + 3) - 1| - 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0((-2((-3x + 3)/(-3x - 3)) - 2)/(-2((-3x + 3)/(-3x - 3)) - 3)) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-2((1x - 3)/(3x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(4((1x - 1)/(-3x))^2 + 4((1x - 1)/(-3x)) - 1)^2 + 2(4((1x - 1)/(-3x))^2 + 4((1x - 1)/(-3x)) - 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-5(3cos(3\u03c0x - 3) - 1)) + 1)/(-1(-5(3cos(3\u03c0x - 3) - 1)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(4(-4x^2 + 3x - 5)^2 - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "733", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(2((-1x + 1)/(1x - 3))^2 - 5((-1x + 1)/(1x - 3)) - 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2((-3(3sin(1\u03c0x + 2) + 1) + 2)/(-3(3sin(1\u03c0x + 2) + 1) - 3)))/(-2((-3(3sin(1\u03c0x + 2) + 1) + 2)/(-3(3sin(1\u03c0x + 2) + 1) - 3)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|((3(2x^2 - 3x - 2) - 2)/(-1(2x^2 - 3x - 2) + 3))| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3sin(1\u03c0(1|x + 3|) + 3) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(4((3x + 3)/(1x - 2))^2 - 1((3x + 3)/(1x - 2)) - 1)^2 - 4(4((3x + 3)/(1x - 2))^2 - 1((3x + 3)/(1x - 2)) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0((-2(3|x - 1| - 3) + 3)/(2(3|x - 1| - 3) + 3)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(-1(3|x - 2| + 3)^2 + 1(3|x - 2| + 3) - 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((-3(2sin(1\u03c0x + 2) + 1) - 2)/(-3(2sin(1\u03c0x + 2) + 1) - 3))| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(1cos(3\u03c0((-3x - 2)/(-2x + 1)) + 3) - 1)^2 - 4(1cos(3\u03c0((-3x - 2)/(-2x + 1)) + 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(-2((3x - 3)/(-3x)) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(4(-4x^2 - 3x + 4) + 1)^2 - 3(4(-4x^2 - 3x + 4) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2sin(3\u03c0((-3x + 2)/(3x + 1)) - 2) - 3)^2 + 3(2sin(3\u03c0((-3x + 2)/(3x + 1)) - 2) - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(1|((1x - 2)/(1x)) + 2| + 2) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-2|((-3x - 1)/(2x + 2)) + 2| + 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(2\u03c0((2(3|x - 2| + 1) - 3)/(-1(3|x - 2| + 1) + 2)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-5(-1sin(1\u03c0x + 1) + 2) + 4) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(-5(1x - 2)^2 + 2(1x - 2) + 4) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1659", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((-2(-3sin(3\u03c0x - 1) - 1) - 2)/(-1(-3sin(3\u03c0x - 1) - 1) + 3)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(2|(-1|x + 1| + 3) - 2| + 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(2\u03c0(-4(-5x + 2)^2 - 3(-5x + 2) + 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1222", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-1sin(2\u03c0(5x^2 - 4x + 4) - 2) - 1) + 2)/(3(-1sin(2\u03c0(5x^2 - 4x + 4) - 2) - 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "977", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(4(-2sin(2\u03c0x - 2) + 3)^2 - 2) + 2)/(-3(4(-2sin(2\u03c0x - 2) + 3)^2 - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-4(-2sin(3\u03c0x - 1) + 3)^2 + 5(-2sin(3\u03c0x - 1) + 3) + 3) - 5 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": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(-1(5x^2 - 5x + 3)^2 + 5(5x^2 - 5x + 3) + 1) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1060", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(5(-3|x - 1| + 3) + 2) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3\u03c0(1|(4x^2 - 2x + 1)|) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1582", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2cos(3\u03c0(-1|x - 3| + 1) + 3) - 1)^2 + 4(-2cos(3\u03c0(-1|x - 3| + 1) + 3) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3sin(3\u03c0(2x^2 - 1) - 1) - 2)^2 + 5(3sin(3\u03c0(2x^2 - 1) - 1) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1050", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0((-1(3x + 3) - 3)/(-2(3x + 3) - 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-3sin(1\u03c0x - 2) + 3) + 1)/(-1(-3sin(1\u03c0x - 2) + 3)))^2 - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(1(-4x^2 - 4x + 5)^2 + 2(-4x^2 - 4x + 5)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-5(3cos(2\u03c0x - 2) + 2) - 3) + 2)/(-1(-5(3cos(2\u03c0x - 2) + 2) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(1\u03c0(-5(2x^2 - 4x + 4)^2 - 4(2x^2 - 4x + 4) + 2) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1280", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(1(-3x^2 - 3x + 2) - 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-2(-2sin(1\u03c0x - 3)))/(2(-2sin(1\u03c0x - 3)) - 1)) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(-2|(2|x - 2| + 3) - 2|) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(1cos(3\u03c0x - 3) + 2) - 1| - 2)^2 + 3(-1|(1cos(3\u03c0x - 3) + 2) - 1| - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1((2(3cos(1\u03c0x + 3) + 3) - 3)/(-3(3cos(1\u03c0x + 3) + 3) + 4)) + 1)/(1((2(3cos(1\u03c0x + 3) + 3) - 3)/(-3(3cos(1\u03c0x + 3) + 3) + 4))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(3\u03c0(-3|(-3|x + 1| + 2) + 3| - 1) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(1\u03c0((3x + 2)/(3x - 1)) + 1) - 2)^2 + 4(-2sin(1\u03c0((3x + 2)/(3x - 1)) + 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(1\u03c0(1x^2 + 4x + 3) + 1) + 2)^2 + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(2cos(2\u03c0(4x - 1) + 2) + 2) - 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(3(-2x^2 - 5x + 3)^2 + 4(-2x^2 - 5x + 3) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(-2|(-4x^2 - 4x + 2) - 3| + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1631", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1(-2cos(2\u03c0x + 2) - 3) - 4) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(2(-1|x - 2| - 2)^2 + 3(-1|x - 2| - 2) - 5) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(1|(-4x^2 + 3x + 4) + 1| - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(5(2x)^2 + 4(2x)) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(2|(2x^2 + 4x + 2) - 1| + 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "951", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-2cos(2\u03c0(2|x - 1| + 3) - 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2cos(2\u03c0(-3x^2 - 1x - 2) - 2))^2 + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1338", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(1cos(3\u03c0((-2x - 2)/(2x - 1)) + 1)) + 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-2|(3sin(2\u03c0x + 3)) - 1|) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-1(-2cos(2\u03c0x - 3)) - 2)/(-3(-2cos(2\u03c0x - 3)) + 2)) + 3)/(-3((-1(-2cos(2\u03c0x - 3)) - 2)/(-3(-2cos(2\u03c0x - 3)) + 2)) + 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(-5x^2 + 4x + 3) - 2|)^2 + 4(-1|(-5x^2 + 4x + 3) - 2|) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-2sin(2\u03c0(2x^2 - 1x - 3) - 3) - 1) + 2)/(2(-2sin(2\u03c0(2x^2 - 1x - 3) - 3) - 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "281", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0(-5((1x + 3)/(1x - 3)) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1(3sin(1\u03c0x) + 3) - 3) + 1)/(-1(1(3sin(1\u03c0x) + 3) - 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(3sin(1\u03c0((1x)/(-3x - 2)) + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2cos(2\u03c0((-2x - 1)/(-2x - 3)) - 3) - 2) - 2)/(-2(2cos(2\u03c0((-2x - 1)/(-2x - 3)) - 3) - 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(3sin(2\u03c0((1x - 1)/(-1x + 2)) + 3) + 3)^2 - 3(3sin(2\u03c0((1x - 1)/(-1x + 2)) + 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(-3(1x^2 + 1x - 3)^2 - 5(1x^2 + 1x - 3) - 3) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1052", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-3sin(3\u03c0(1x - 5) + 3) + 3)^2 + 1(-3sin(3\u03c0(1x - 5) + 3) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-4(2sin(1\u03c0x - 2))^2 - 4(2sin(1\u03c0x - 2)) - 2) - 3)/(1(-4(2sin(1\u03c0x - 2))^2 - 4(2sin(1\u03c0x - 2)) - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-1(-2cos(2\u03c0x - 2) + 3)^2 + 1(-2cos(2\u03c0x - 2) + 3) - 1) - 2)/(-1(-1(-2cos(2\u03c0x - 2) + 3)^2 + 1(-2cos(2\u03c0x - 2) + 3) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-1(5x)^2 - 1(5x) + 5)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1(3|x - 2| - 1)^2 - 5(3|x - 2| - 1) - 4)^2 - 4(1(3|x - 2| - 1)^2 - 5(3|x - 2| - 1) - 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3cos(1\u03c0(-1x + 2) - 1) - 2)^2 - 4(3cos(1\u03c0(-1x + 2) - 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3sin(2\u03c0(5x - 3) + 2) - 2)^2 + 2(3sin(2\u03c0(5x - 3) + 2) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(1|(1x^2 - 5x - 1) - 2| + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(2((-3x - 3)/(-2x - 1))^2 - 4((-3x - 3)/(-2x - 1)) - 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-4(-5x^2 + 3x + 3)^2 + 4(-5x^2 + 3x + 3) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(3|(5x^2 - 1x - 2) - 3| - 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(2|(-5x^2 + 1x + 2) - 2| - 1)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(3\u03c0(-2(4x + 3)^2 + 4(4x + 3) - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1212", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0((1(-4x + 1) + 3)/(3(-4x + 1) - 2)) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0((2(-3|x|) - 1)/(3(-3|x|) + 3))) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(-5(2x - 2)^2 + 3(2x - 2) + 2)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1110", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(3cos(2\u03c0(3|x + 1| + 1) + 2)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(4(2sin(3\u03c0x + 3))^2 - 5(2sin(3\u03c0x + 3)) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(2\u03c0(1|(3|x + 3| + 3) - 2|) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1(1sin(3\u03c0x - 3) - 3) - 3)| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(3sin(1\u03c0(-4x^2 + 2x + 2) - 2) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "613", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0(4(2|x - 2| - 3)^2 - 3(2|x - 2| - 3) + 4) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "878", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((2(-1x^2 - 4x + 4) - 2)/(-1(-1x^2 - 4x + 4) - 1))^2 - 2((2(-1x^2 - 4x + 4) - 2)/(-1(-1x^2 - 4x + 4) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3cos(2\u03c0(-4x - 3) + 3) - 1)^2 - 3(3cos(2\u03c0(-4x - 3) + 3) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-5(3|x - 3| - 2)^2 - 5(3|x - 3| - 2) + 4) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(2\u03c0(1|(3x^2 + 2x + 2)| + 2)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1076", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((-3(1x^2 - 2x - 3))/(3(1x^2 - 2x - 3) - 1)) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(3sin(1\u03c0((1x - 2)/(-2x - 1)) + 1) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-2cos(3\u03c0(1x - 1) + 2))^2 + 2(-2cos(3\u03c0(1x - 1) + 2)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-2(3sin(3\u03c0x - 1) + 2) + 1) + 1 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": "How many zeros does the function f(x) = -2(1(1|x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(-1(3x + 3)^2 - 1(3x + 3) - 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1696", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0((3(2|x - 3| - 2) - 3)/(2(2|x - 3| - 2) - 1)) + 2) + 3 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 zeros does the function f(x) = (-2(-1cos(3\u03c0((-3x)/(2x + 3)) + 2) + 2) + 3)/(2(-1cos(3\u03c0((-3x)/(2x + 3)) + 2) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((-2(2x^2 - 5x - 4) + 1)/(-2(2x^2 - 5x - 4)))^2 - 1((-2(2x^2 - 5x - 4) + 1)/(-2(2x^2 - 5x - 4))) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(-4(3x + 5)^2 + 2(3x + 5) - 3) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1203", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(5(2|x - 2|)^2 - 1(2|x - 2|) - 4)^2 + 1(5(2|x - 2|)^2 - 1(2|x - 2|) - 4) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(3sin(1\u03c0(-2|x - 2| + 3)) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1|(-5x^2 - 3x + 3) - 1|) - 2)/(1(-1|(-5x^2 - 3x + 3) - 1|)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(1(-3cos(2\u03c0x + 1) + 1) - 3)^2 + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((2(3sin(2\u03c0x + 1) + 1))/(1(3sin(2\u03c0x + 1) + 1) - 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(3sin(2\u03c0(-5x + 3) + 1) + 3)^2 - 4(3sin(2\u03c0(-5x + 3) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-3(3cos(2\u03c0x - 3) - 3))/(2(3cos(2\u03c0x - 3) - 3) - 1)) + 2| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-2|(3|x + 1|)| + 2)^2 + 1(-2|(3|x + 1|)| + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(4(-2cos(1\u03c0x - 3) - 2) + 2) - 1)/(3(4(-2cos(1\u03c0x - 3) - 2) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(2(3x^2 + 4x + 3) - 5)^2 - 3(2(3x^2 + 4x + 3) - 5) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-3(5x - 5)^2 - 3) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1497", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-4(2cos(3\u03c0x - 1) - 2)^2 + 4(2cos(3\u03c0x - 1) - 2) + 5) + 1 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": "How many solutions does the equation -1cos(2\u03c0(-2|(-1x^2 - 1x - 4) + 2| + 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3((-3(3sin(2\u03c0x + 3) + 2) + 1)/(-1(3sin(2\u03c0x + 3) + 2) - 2)) - 3)/(3((-3(3sin(2\u03c0x + 3) + 2) + 1)/(-1(3sin(2\u03c0x + 3) + 2) - 2)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(-2(2|x + 2| - 2) - 3) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(2cos(3\u03c0((1x + 2)/(-2x - 2)) + 3) - 1) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-4(1cos(3\u03c0x + 1) + 1) - 2) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1((1x - 1)/(-3x - 2))^2 - 5((1x - 1)/(-3x - 2)))^2 - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(2cos(2\u03c0(2|x - 2| + 3) + 1) - 2)| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(2\u03c0(3|(2x^2 - 1x - 3) - 2| - 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1585", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1|(1sin(2\u03c0x + 1) - 3) + 1| - 3) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(1sin(1\u03c0(5x^2 + 3)))| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1068", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0(4(2|x + 2| + 3)^2 - 2(2|x + 2| + 3) + 5) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1506", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3cos(2\u03c0(-1x^2 - 3x + 1) + 3) - 1) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-2|(-2|x| + 2) + 2| + 2)^2 - 4(-2|(-2|x| + 2) + 2| + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(-3|(5x^2 + 4x - 5) - 2| + 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3cos(2\u03c0(2x + 3) + 1) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1|(-2|x| + 3) + 2| + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(5(-3x^2 - 4x + 5) + 4) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(3cos(1\u03c0(5x - 4) - 2) + 2) - 1)/(3(3cos(1\u03c0(5x - 4) - 2) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-2(3x^2 - 5x - 3)^2 + 5(3x^2 - 5x - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((2(-1x^2 + 1x + 2) - 1)/(-1(-1x^2 + 1x + 2) + 2)) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3sin(3\u03c0(2|x|) + 2)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(-2|((2x)/(-2x - 1)) - 3| - 3) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-2(-1cos(3\u03c0x + 3) - 2) - 1)/(-3(-1cos(3\u03c0x + 3) - 2) - 3)) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(1((-3x - 2)/(1x))^2 - 5((-3x - 2)/(1x)) + 5) - 2) - 1 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": "How many zeros does the function f(x) = 2cos(3\u03c0((-1((2x)/(-3x - 3)) - 3)/(-1((2x)/(-3x - 3)) - 1)) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-4((-1x - 2)/(1x))^2 - 2((-1x - 2)/(1x)) - 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(-2cos(2\u03c0x + 3) - 2)^2 + 3(-2cos(2\u03c0x + 3) - 2) - 5) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(4(-1|x + 2| + 1)^2 + 1(-1|x + 2| + 1) - 3) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3|(-2x^2 + 5x + 4)| + 3))/(2(-3|(-2x^2 + 5x + 4)| + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(5(-4x^2 + 1x + 3) - 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0(-2|(2|x + 2| - 3) - 1| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(-5(4x^2 + 5x - 1)^2 - 3(4x^2 + 5x - 1) - 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-2(2cos(2\u03c0x + 3)) + 1)/(-3(2cos(2\u03c0x + 3)) - 2))^2 - 4((-2(2cos(2\u03c0x + 3)) + 1)/(-3(2cos(2\u03c0x + 3)) - 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-1(3cos(2\u03c0x - 1) - 2)^2 + 5(3cos(2\u03c0x - 1) - 2) + 2) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0(-1((-3x - 1)/(3x + 2)) - 4) - 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3sin(2\u03c0(-1x) - 2) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-2cos(3\u03c0(5x^2 + 5x) + 3))^2 - 2(-2cos(3\u03c0(5x^2 + 5x) + 3)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1490", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(3|(-3|x - 1| - 1) - 2| - 1) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(1((-3x)/(-2x + 3)) + 3) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-2cos(3\u03c0(-3x) - 3) + 1)^2 - 2(-2cos(3\u03c0(-3x) - 3) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-3|(2|x + 2| - 1) - 2| - 1) + 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 number of x-intercepts of the function f(x) = (-3(-2|(-5x^2 - 3x - 1) + 1|) - 2)/(3(-2|(-5x^2 - 3x - 1) + 1|) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-1sin(2\u03c0(-3x^2 + 4x + 5) - 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(3(2|x| - 3))^2 - 5(3(2|x| - 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(4(-2|x - 3| + 2)^2 - 5(-2|x - 3| + 2) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-2|((1x - 2)/(-3x + 4))| + 3)^2 + 3(-2|((1x - 2)/(-3x + 4))| + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2sin(3\u03c0(2|x + 3| + 1) - 1) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-1(3sin(1\u03c0x + 1) - 2)^2 + 5(3sin(1\u03c0x + 1) - 2) - 5) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2((2(1|x + 1| - 3) - 2)/(3(1|x + 1| - 3) - 1))^2 + 3((2(1|x + 1| - 3) - 2)/(3(1|x + 1| - 3) - 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((-1(3x^2 - 2x - 2) + 3)/(-1(3x^2 - 2x - 2) - 3))^2 + 4((-1(3x^2 - 2x - 2) + 3)/(-1(3x^2 - 2x - 2) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(3|((2x + 2)/(-1x - 2))| + 1) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-1|((-2x - 1)/(2x - 1))| - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(-3(-3|x + 3|)^2 + 1(-3|x + 3|) - 5) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1283", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-1|(1sin(3\u03c0x + 2) - 2)| - 3) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0(4(-3|x - 2| - 3)^2 - 5(-3|x - 2| - 3) + 3) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1326", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-2sin(2\u03c0((2x)/(2x - 3))) - 2)^2 + 5(-2sin(2\u03c0((2x)/(2x - 3))) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1e^(2(-5x^2 + 4x + 1))) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(2|(3x^2 + 3x + 5) + 1| - 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1698", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-4(3sin(2\u03c0x - 1) + 3) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((-1(-3cos(1\u03c0x + 3) + 2) + 3)/(-3(-3cos(1\u03c0x + 3) + 2) - 3)) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(-3|((3x - 2)/(-1x + 3)) - 2| + 1) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(2((2x + 3)/(-3x - 3))^2 - 2((2x + 3)/(-3x - 3)) - 1) - 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(1(1|x + 1| + 3) + 5)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-1(2x^2 - 5x - 1)^2 + 4)^2 + 3(-1(2x^2 - 5x - 1)^2 + 4) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(5(3cos(1\u03c0x + 2) - 1) - 3)^2 - 3(5(3cos(1\u03c0x + 2) - 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(3(2x^2 - 2x - 3)^2 - 4(2x^2 - 2x - 3) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(2cos(1\u03c0(5x + 2) + 3) - 3) + 2| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3|(-2|x + 1|) + 3| + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-5((2x - 2)/(2x - 1))^2 - 1((2x - 2)/(2x - 1)) + 5) + 3| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(-3x^2 + 5x + 5) - 1)/(-2(-3x^2 + 5x + 5) - 1))^2 - 2((-3(-3x^2 + 5x + 5) - 1)/(-2(-3x^2 + 5x + 5) - 1)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3sin(2\u03c0(2x + 4) + 2) - 3) + 3)/(1(3sin(2\u03c0(2x + 4) + 2) - 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(1|(-1|x - 1| + 3)| - 1) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-2|(-1sin(2\u03c0x) + 3) - 2| + 3)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(-2|(-2|x - 3| + 3) + 3|) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2cos(3\u03c0(-2x^2 + 2x + 5) - 1) + 2)^2 + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1162", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3(-2|x + 1| + 3)^2 - 1(-2|x + 1| + 3) - 3) + 2)/(-3(3(-2|x + 1| + 3)^2 - 1(-2|x + 1| + 3) - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-2|(2cos(3\u03c0x - 2) + 3) - 1| - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(3(-3cos(2\u03c0x) - 3)^2 + 3(-3cos(2\u03c0x) - 3) - 2) + 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(-5x^2 - 2x + 3) + 2)^2 + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2(-2sin(3\u03c0x) - 3) + 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(1|(1cos(2\u03c0x - 3) + 3) - 2| - 2)^2 - 1(1|(1cos(2\u03c0x - 3) + 3) - 2| - 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(-1((-2x - 1)/(-1x + 2)) - 2) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0((-1(2x - 1) + 3)/(-1(2x - 1))) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1((3x + 3)/(-1x + 2))^2 + 5((3x + 3)/(-1x + 2)) - 1) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3\u03c0(1(-1x^2 + 4x + 5)^2 - 4(-1x^2 + 4x + 5) - 4) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1050", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(2(1x^2 - 5x - 1)^2 - 1(1x^2 - 5x - 1) + 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1269", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3((-3x + 2)/(3x + 2))^2 - 2((-3x + 2)/(3x + 2)) + 3)^2 + 5(-3((-3x + 2)/(3x + 2))^2 - 2((-3x + 2)/(3x + 2)) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((2(4x^2 + 3x - 1) + 2)/(3(4x^2 + 3x - 1) - 2))^2 + 3((2(4x^2 + 3x - 1) + 2)/(3(4x^2 + 3x - 1) - 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(-2|((-3x - 3)/(-1x + 2)) + 2| - 2) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(-3|(-2x^2 - 5x - 2) - 3| - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1166", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(4(5x + 1) - 4) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2sin(3\u03c0(5x - 1) - 3) - 3)^2 - 3(-2sin(3\u03c0(5x - 1) - 3) - 3) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-3|(-5x^2 - 1x + 3) + 2| + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(-2(1x^2 + 1x - 1) - 5) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(5(-4x^2 - 2x + 1)^2 - 5(-4x^2 - 2x + 1) + 1)^2 - 3(5(-4x^2 - 2x + 1)^2 - 5(-4x^2 - 2x + 1) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1sin(3\u03c0((1x)/(-3x - 1)) + 3)) + 3)/(1(1sin(3\u03c0((1x)/(-3x - 1)) + 3)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-3cos(3\u03c0(2|x| + 1) + 2) + 1) - 1)/(-2(-3cos(3\u03c0(2|x| + 1) + 2) + 1) - 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 number of x-intercepts of the function f(x) = -2cos(1\u03c0((2(2x - 1) + 3)/(-1(2x - 1))) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3cos(3\u03c0(5x^2 + 4x + 4) + 1) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1319", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(3sin(3\u03c0(3|x - 1| - 1) + 3) - 3)^2 + 1(3sin(3\u03c0(3|x - 1| - 1) + 3) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(2(5x^2 + 4x)^2 + 4(5x^2 + 4x) - 1)| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-4(-2sin(2\u03c0x - 3)) - 1) + 2)/(2(-4(-2sin(2\u03c0x - 3)) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(1|(-3|x| - 1) - 2| - 3) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((-2(1x^2 + 5x - 3) - 3)/(-3(1x^2 + 5x - 3) - 1)) - 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(2(3sin(2\u03c0x - 1)) - 5) - 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(-2|(2|x - 2| + 3) - 1| + 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(1(-1x^2 - 1) + 4) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2(1|x - 1| - 3)^2 + 4))/(-2(-2(1|x - 1| - 3)^2 + 4) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2((3(-3cos(3\u03c0x) + 3))/(2(-3cos(3\u03c0x) + 3) + 3)))/(3((3(-3cos(3\u03c0x) + 3))/(2(-3cos(3\u03c0x) + 3) + 3)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-2sin(2\u03c0(-1x - 1) + 3) + 2)^2 + 1(-2sin(2\u03c0(-1x - 1) + 3) + 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2((-3(2|x + 1| - 1))/(-3(2|x + 1| - 1) - 2))^2 - 3((-3(2|x + 1| - 1))/(-3(2|x + 1| - 1) - 2)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3|(-1|x + 3| + 2) + 2| + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0(5((2x - 2)/(2x + 2)) - 5)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-3sin(2\u03c0((-2x)/(-3x + 4)) - 1)) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3sin(2\u03c0((3x + 1)/(2x)) + 1) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0(-2|((1x - 3)/(1x + 1)) - 2| - 3) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(3|(2x^2 + 2x - 3) + 1| - 1)^2 + 5(3|(2x^2 + 2x - 3) + 1| - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-1cos(2\u03c0(5x^2 - 1x - 3) + 1) + 3)^2 - 5(-1cos(2\u03c0(5x^2 - 1x - 3) + 1) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1353", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-3sin(3\u03c0(-1x^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": "289", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1cos(3\u03c0((-3x + 2)/(-2x - 2)) - 3) + 1) + 2)/(2(1cos(3\u03c0((-3x + 2)/(-2x - 2)) - 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(3cos(3\u03c0(-2|x - 3| + 3) - 3) - 2) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-5(-4x + 1)^2 - 3(-4x + 1) - 2) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0(-1(5x^2 + 5x + 5)^2 + 1) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1251", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(-3sin(2\u03c0x + 2) + 2) - 1) - 1)/(3(-2(-3sin(2\u03c0x + 2) + 2) - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(1((-1x + 1)/(1x + 2))^2 + 3((-1x + 1)/(1x + 2)))) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0((2(-1x + 1) - 3)/(3(-1x + 1) - 2)) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-4(2cos(3\u03c0x + 2) - 1)^2 + 3(2cos(3\u03c0x + 2) - 1) + 5) + 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": "How many zeros does the function f(x) = (3(5(-1x^2 + 3x + 2)^2 - 3(-1x^2 + 3x + 2) - 5) - 3)/(-2(5(-1x^2 + 3x + 2)^2 - 3(-1x^2 + 3x + 2) - 5) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(1(-1cos(1\u03c0x + 2) - 3) + 4) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(2\u03c0(-5(3|x - 2| - 3)^2 - 5(3|x - 2| - 3) + 4) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1506", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(-2|(1x + 2) + 2| - 1) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(2(1|x - 3| - 1) + 5) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(2\u03c0(1|(-3x + 2) - 3| + 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0(-1|(3x - 3) - 1| + 1) - 2) + 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 number of x-intercepts of the function f(x) = -3cos(1\u03c0(-5(-3|x + 1| - 1) - 2) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0((3(2x - 5) - 3)/(2(2x - 5) + 3)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(2sin(3\u03c0((-1x - 1)/(-3x)) + 1) + 1) + 1| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2cos(3\u03c0((-2x + 3)/(1x)) - 1) + 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(3(-3|x - 2| + 2) + 3) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(1(-2x^2 - 4x + 3) - 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(1\u03c0(5(-1x - 4) + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(3|((2x)/(-1x - 3)) + 2| - 2) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3sin(2\u03c0(4x + 1) - 1) - 1) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-1sin(3\u03c0(4x^2 - 3x + 5) + 1) - 2)^2 + 2(-1sin(3\u03c0(4x^2 - 3x + 5) + 1) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1132", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3cos(3\u03c0(3|x - 1| - 3) - 3) + 3)^2 + 1(3cos(3\u03c0(3|x - 1| - 3) - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1(3x^2 - 5x - 4)^2 + 2(3x^2 - 5x - 4) + 1)^2 - 3(-1(3x^2 - 5x - 4)^2 + 2(3x^2 - 5x - 4) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1(2cos(2\u03c0x - 2) - 1)^2 - 5(2cos(2\u03c0x - 2) - 1) - 1)^2 + 1(-1(2cos(2\u03c0x - 2) - 1)^2 - 5(2cos(2\u03c0x - 2) - 1) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-4(-1x^2 + 4x + 2)^2 + 3(-1x^2 + 4x + 2) + 1) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1167", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(1(1x^2 + 3x + 4)^2 - 5(1x^2 + 3x + 4) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1288", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(1(2|x| - 1)^2 + 5(2|x| - 1) + 3)^2 + 1(1(2|x| - 1)^2 + 5(2|x| - 1) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-3cos(2\u03c0(5x + 5) + 1) + 1)| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(3\u03c0(-2(-1x - 5)^2 - 2(-1x - 5) + 1) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0((2(1x^2 - 5x + 2) + 3)/(1(1x^2 - 5x + 2) + 1)) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(-5(4x + 3)^2 - 1(4x + 3) - 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1445", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3(2cos(2\u03c0x)) + 3)^2 - 5(3(2cos(2\u03c0x)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(3\u03c0(4(1|x - 2|) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(5(1x^2 + 3x - 4)^2 + 1(1x^2 + 3x - 4) - 5) + 1)/(-1(5(1x^2 + 3x - 4)^2 + 1(1x^2 + 3x - 4) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(1cos(3\u03c0(1x^2 + 4x + 1) - 3) - 1)^2 + 4(1cos(3\u03c0(1x^2 + 4x + 1) - 3) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(-4(-5x^2 + 3x)^2 + 3(-5x^2 + 3x) - 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-4((-1x + 3)/(1x))^2 + 3((-1x + 3)/(1x)) + 5) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-2(4x^2 - 3x + 4)^2 + 1(4x^2 - 3x + 4) - 5) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1347", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0(2((2x - 1)/(-2x + 3)) + 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(2\u03c0(-2|((2x)/(-3x + 2)) + 2| - 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-5(2|x| - 3) + 5)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(3(-2x^2 - 2x + 4) - 5) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(1((1x + 3)/(3x - 2))^2 + 2((1x + 3)/(3x - 2)) - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(1((-1x)/(-1x + 2))^2 - 5) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(2|(-1x - 3) + 3| + 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2sin(3\u03c0(3x^2 - 5x) - 2) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1389", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(-4(-3x - 4) - 3) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(3(-1x^2 + 4x - 1) - 5) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1356", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3e^(-1(3|(-1x^2 - 5x) - 3| - 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0((-2((3x - 1)/(1x)))/(-3((3x - 1)/(1x)) - 1)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(3sin(2\u03c0(-1|x - 3| + 2) + 3) - 3)^2 + 4(3sin(2\u03c0(-1|x - 3| + 2) + 3) - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(1(-2cos(3\u03c0x))^2 - 5(-2cos(3\u03c0x)) - 4) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-4(2|x| - 3)^2 + 1(2|x| - 3) + 3)^2 - 4(-4(2|x| - 3)^2 + 1(2|x| - 3) + 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-3(2sin(1\u03c0x - 2)) - 2))/(3(-3(2sin(1\u03c0x - 2)) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((-1(-1x^2 + 3x + 5) + 1)/(-1(-1x^2 + 3x + 5) - 2))^2 + 2((-1(-1x^2 + 3x + 5) + 1)/(-1(-1x^2 + 3x + 5) - 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(2|(-1x^2 + 2x + 4) - 3| - 1) - 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1cos(1\u03c0((3x)/(2x - 1)) + 3) - 2) + 2)/(1(1cos(1\u03c0((3x)/(2x - 1)) + 3) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(3|(-4x^2 + 5x + 3) + 3| + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1577", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(2(-5x^2 + 4x - 5)^2 - 5(-5x^2 + 4x - 5) - 2) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2((3(3sin(1\u03c0x) + 2))/(1(3sin(1\u03c0x) + 2) - 2)) - 2)/(2((3(3sin(1\u03c0x) + 2))/(1(3sin(1\u03c0x) + 2) - 2)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3((-3(-2sin(3\u03c0x - 2) - 1) - 2)/(2(-2sin(3\u03c0x - 2) - 1))) - 1)/(-2((-3(-2sin(3\u03c0x - 2) - 1) - 2)/(2(-2sin(3\u03c0x - 2) - 1))) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(3cos(3\u03c0(-2|x - 1| + 1) + 2) + 2) + 3)/(2(3cos(3\u03c0(-2|x - 1| + 1) + 2) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2(2sin(3\u03c0x + 1) + 3)^2 + 2(2sin(3\u03c0x + 1) + 3) + 4) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2|(5x^2 + 1x - 2) - 2| - 2)^2 + 5(2|(5x^2 + 1x - 2) - 2| - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3sin(2\u03c0(-5x + 4) + 1) + 1)^2 + 1(-3sin(2\u03c0(-5x + 4) + 1) + 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-1|(1sin(2\u03c0x) - 3) - 1| + 3) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1(-2sin(1\u03c0x - 3) + 1)^2 - 5(-2sin(1\u03c0x - 3) + 1) + 5)^2 - 2(-1(-2sin(1\u03c0x - 3) + 1)^2 - 5(-2sin(1\u03c0x - 3) + 1) + 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(3sin(1\u03c0(5x + 5) + 3) + 2)^2 + 4(3sin(1\u03c0(5x + 5) + 3) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(1\u03c0(3(3|x| - 3) - 4) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0(-1|(-1x^2 + 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": "600", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((-1(1|x + 1| - 3) - 2)/(2(1|x + 1| - 3) + 1)) + 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-2cos(1\u03c0(-1x + 5) - 2) - 2)^2 - 5(-2cos(1\u03c0(-1x + 5) - 2) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2|(3x^2 - 2x - 1) - 3| + 3)^2 + 5(2|(3x^2 - 2x - 1) - 3| + 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(3|(-1x - 5) + 2| - 3)| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(2|(1|x - 1| + 3) - 2| + 1) - 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": "How many solutions does the equation -3(-1(3sin(3\u03c0x - 2) - 1) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-1|(-2x^2 - 1x + 4) - 1|) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(3sin(3\u03c0(-4x^2 + 4x - 2)) + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1278", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(4(2cos(3\u03c0x + 3)) - 3) + 3)/(-3(4(2cos(3\u03c0x + 3)) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(1(2sin(2\u03c0x + 1) - 1)^2 + 4(2sin(2\u03c0x + 1) - 1) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(4(2cos(2\u03c0x) - 1)^2 - 2(2cos(2\u03c0x) - 1))^2 + 1(4(2cos(2\u03c0x) - 1)^2 - 2(2cos(2\u03c0x) - 1)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0((2(-1x - 2) - 2)/(-3(-1x - 2) - 1)) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((-1(-3sin(1\u03c0x - 3) + 2) - 1)/(2(-3sin(1\u03c0x - 3) + 2) + 1))^2 + 2((-1(-3sin(1\u03c0x - 3) + 2) - 1)/(2(-3sin(1\u03c0x - 3) + 2) + 1)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1(2sin(3\u03c0x) - 2)^2 + 2(2sin(3\u03c0x) - 2) + 4) + 3)/(-2(1(2sin(3\u03c0x) - 2)^2 + 2(2sin(3\u03c0x) - 2) + 4) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3cos(3\u03c0(4x + 5) + 2) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1\u03c0(3(-3x^2 + 1x)^2 - 2(-3x^2 + 1x) + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(2|(-3x + 5) + 3|) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0(-2(-3|x + 1| - 1)) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(2|(-4x^2 + 1x + 2) - 1| - 1) + 1)/(1(2|(-4x^2 + 1x + 2) - 1| - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(3sin(3\u03c0(1|x| - 3) + 3) - 1)^2 + 1(3sin(3\u03c0(1|x| - 3) + 3) - 1) + 4 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": "Determine the number of values x in [-10, 10] where f(x) = 2|(-2e^(2(-2x^2 + 5x - 5)) + 1) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(1|(-2|x + 1| + 3) + 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": "How many solutions does the equation 1(2(4x^2 - 5x - 5)^2 - 5(4x^2 - 5x - 5) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1\u03c0(1|(-1|x - 2|) + 1| + 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-4(-3sin(3\u03c0x + 2) - 2)^2 + 5(-3sin(3\u03c0x + 2) - 2) + 5) + 1)/(1(-4(-3sin(3\u03c0x + 2) - 2)^2 + 5(-3sin(3\u03c0x + 2) - 2) + 5) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(1\u03c0(3(-1|x - 3| + 3)^2 - 2(-1|x - 3| + 3) + 4) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "420", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(-2((-1x - 3)/(-3x + 1)) + 5) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-3(1x^2 - 2x - 1) - 5) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0(2(1x - 1)^2 - 1(1x - 1) - 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "794", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(1|(2x^2 - 2x - 2) + 3|) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "521", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-3(1|x - 2| - 3) - 1)/(-1(1|x - 2| - 3) - 3))^2 + 1((-3(1|x - 2| - 3) - 1)/(-1(1|x - 2| - 3) - 3)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-4(-1x^2 - 3x + 4) + 3)^2 + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(2\u03c0(-1(1|x + 2|)^2 - 2(1|x + 2|) - 4)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-3cos(3\u03c0(-4x - 3) + 1) - 3))/(-1(-3cos(3\u03c0(-4x - 3) + 1) - 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(1((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1))) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2sin(1\u03c0((-1x - 3)/(3x + 3)) - 1) + 2)^2 + 3(2sin(1\u03c0((-1x - 3)/(3x + 3)) - 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 zeros does the function f(x) = 4((2(2cos(2\u03c0x - 2)) + 3)/(-3(2cos(2\u03c0x - 2)) - 3))^2 + 3((2(2cos(2\u03c0x - 2)) + 3)/(-3(2cos(2\u03c0x - 2)) - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(5(2x^2 + 2x - 5) + 5)^2 - 4(5(2x^2 + 2x - 5) + 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-4(2sin(2\u03c0x + 3) + 1)^2 + 1(2sin(2\u03c0x + 3) + 1) + 4) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(5(-1|x - 2| + 2)^2 - 1(-1|x - 2| + 2)) - 2)/(2(5(-1|x - 2| + 2)^2 - 1(-1|x - 2| + 2)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-2|(-1sin(3\u03c0x + 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": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(-3|(3|x - 3| + 3) + 2| - 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-2(-4x + 4)^2 - 5(-4x + 4) + 1)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3|(-2sin(2\u03c0x + 2) - 2) + 2| + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2sin(1\u03c0(1x + 3) + 3) + 1) - 1)/(-1(2sin(1\u03c0(1x + 3) + 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2((-1(-3cos(3\u03c0x - 1) + 3))/(2(-3cos(3\u03c0x - 1) + 3) - 3)) + 2)/(-3((-1(-3cos(3\u03c0x - 1) + 3))/(2(-3cos(3\u03c0x - 1) + 3) - 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0(-3|(-1x - 5) - 3| - 2) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-2(-2x^2 - 1x - 3) + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-3(2|x - 1| + 1) + 5) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2cos(2\u03c0(-1|x + 3|) - 2) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(1sin(3\u03c0(-2|x - 3| + 3) + 2) + 2) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0((-1(3x - 3) - 3)/(2(3x - 3) - 1)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3(-2e^(1x) + 2)^2 - 5(-2e^(1x) + 2))^2 - 1(-3(-2e^(1x) + 2)^2 - 5(-2e^(1x) + 2)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(4(-1x + 1)^2 - 3(-1x + 1) - 1)^2 - 5(4(-1x + 1)^2 - 3(-1x + 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(1|(3|x + 1| - 3) - 3| - 3))/(-1(1|(3|x + 1| - 3) - 3| - 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-2|(-1x^2 - 5x)| - 2) - 3)/(2(-2|(-1x^2 - 5x)| - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3(-3cos(1\u03c0x + 3) - 2) - 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1(-2x^2 + 5x + 5)^2 + 3(-2x^2 + 5x + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1(3|x + 3| - 3)^2 - 5(3|x + 3| - 3) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1(-5x + 5)^2 - 5(-5x + 5) - 1)| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(1cos(2\u03c0(-4x - 3) - 2) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-5(2sin(2\u03c0x + 1) + 2)^2 + 3(2sin(2\u03c0x + 1) + 2) - 3) + 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": "How many zeros does the function f(x) = -1(1sin(2\u03c0((3x)/(3x - 2)) - 3))^2 - 3(1sin(2\u03c0((3x)/(3x - 2)) - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(1(1|x - 2| + 1) + 2) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1) - 1)/(-3(3(-1x^2 - 2x + 2)^2 - 5(-1x^2 - 2x + 2) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-1|(3x^2 + 2x)| + 2)^2 - 3(-1|(3x^2 + 2x)| + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(-1((1x + 3)/(1x - 3))^2 - 3((1x + 3)/(1x - 3)) - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "297", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(3sin(3\u03c0(3|x + 1|) - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0((-1((1x)/(-3x + 4)) + 3)/(-2((1x)/(-3x + 4)) - 2)) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1((-1(2sin(1\u03c0x) - 1) + 1)/(1(2sin(1\u03c0x) - 1))) + 1)/(1((-1(2sin(1\u03c0x) - 1) + 1)/(1(2sin(1\u03c0x) - 1)))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-2|(1|x + 3|)| + 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2sin(2\u03c0(2|x - 1| - 3) - 1) + 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2|(-3|x + 3| + 1) + 2| + 1)^2 - 5(-2|(-3|x + 3| + 1) + 2| + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(5(2sin(2\u03c0x + 1) - 1) - 3) - 3)/(1(5(2sin(2\u03c0x + 1) - 1) - 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((2((-1x - 1)/(1x + 3)) - 2)/(-1((-1x - 1)/(1x + 3)) - 2)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(-4(1|x - 1| - 2)^2 - 5(1|x - 1| - 2) + 4) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0((2((-1x - 2)/(3x + 2)) - 2)/(-1((-1x - 2)/(3x + 2)) + 2))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0((-3((1x + 2)/(2x)) + 1)/(-3((1x + 2)/(2x))))) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(3\u03c0((2x - 3)/(-1x + 3)) + 1) - 2) - 2)/(-2(-3sin(3\u03c0((2x - 3)/(-1x + 3)) + 1) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(4(-3|x|)) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-3cos(3\u03c0(-1|x - 3| - 2) + 1) - 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1(-3cos(3\u03c0x - 1) + 1)^2 + 3(-3cos(3\u03c0x - 1) + 1) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(2(5x + 4) - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(4(3x^2 - 5x - 4) + 4) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1233", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(3|(-1x^2 + 3x) - 3|) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0((1(-4x + 2) - 1)/(-3(-4x + 2))) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(1cos(2\u03c0(-1x^2 - 3x - 5) + 2) + 1) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "408", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-5(-2x^2 + 2)^2 - 1(-2x^2 + 2) - 1) - 1)/(-1(-5(-2x^2 + 2)^2 - 1(-2x^2 + 2) - 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|((3(-3cos(3\u03c0x - 3)) + 3)/(1(-3cos(3\u03c0x - 3)) + 2)) - 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(1(4x^2 + 5x - 5)) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(3\u03c0(-3(-1|x - 3| - 3)^2 + 2(-1|x - 3| - 3) - 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1884", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(5(2cos(3\u03c0x + 3) + 1)^2 + 3(2cos(3\u03c0x + 3) + 1) - 2)^2 + 2(5(2cos(3\u03c0x + 3) + 1)^2 + 3(2cos(3\u03c0x + 3) + 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-3(-4x^2 + 3x - 1) + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1561", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-1(-4x^2 + 5x + 2)^2 - 3(-4x^2 + 5x + 2) + 2) + 3)/(2(-1(-4x^2 + 5x + 2)^2 - 3(-4x^2 + 5x + 2) + 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(-5((2x + 1)/(-1x - 1))^2 + 2((2x + 1)/(-1x - 1)) - 5) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2sin(2\u03c0(1x^2 + 2x + 1)) - 2))/(-1(2sin(2\u03c0(1x^2 + 2x + 1)) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "193", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0((-3(1x - 1))/(-2(1x - 1) + 3)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(3|(-3sin(2\u03c0x + 1) - 1)| - 2) - 2)/(2(3|(-3sin(2\u03c0x + 1) - 1)| - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-1(-1|x| - 1) - 2)^2 - 5(-1(-1|x| - 1) - 2) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(2|(3|x + 2| + 3) - 1|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-1sin(1\u03c0(-2x + 5) + 2)) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(-2|(1|x + 1|) + 2| - 2) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2|(-2sin(1\u03c0x - 1) - 2) + 1| + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-3cos(1\u03c0((1x - 2)/(-2x - 3))) - 1) + 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(2((-2x + 3)/(2x - 1)) - 2) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-2|(4x - 4)| + 2)| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1(1x^2 + 2x + 1) - 4)^2 + 3(1(1x^2 + 2x + 1) - 4) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-5(4x^2 - 2x + 1)^2 - 4(4x^2 - 2x + 1) + 4) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(2cos(1\u03c0(1x)) + 2) + 1)/(2(2cos(1\u03c0(1x)) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(-2|(-5x + 2) - 1| + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(1(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 3) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((-1(-4x^2 + 4x + 3) + 1)/(2(-4x^2 + 4x + 3) - 3))^2 - 2((-1(-4x^2 + 4x + 3) + 1)/(2(-4x^2 + 4x + 3) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(2(5x + 1)^2 + 1(5x + 1) + 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1194", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-3(2cos(2\u03c0x - 3) + 1) + 5) + 1)/(1(-3(2cos(2\u03c0x - 3) + 1) + 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(3((3x - 1)/(2x + 3))^2 + 3((3x - 1)/(2x + 3)) - 3) + 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(1e^(-1(4x^2 + 3x - 2)) - 3)^2 - 2(1e^(-1(4x^2 + 3x - 2)) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0(-1|(5x^2 - 2x - 3) - 2| + 2)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "434", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-3(2x + 1)^2 - 2(2x + 1) + 5) + 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(5(5x - 2) - 5) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1\u03c0(-1((2x - 2)/(-2x + 1)) - 4) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((3(2sin(1\u03c0x + 2) + 2) - 3)/(-2(2sin(1\u03c0x + 2) + 2) + 3))^2 - 5((3(2sin(1\u03c0x + 2) + 2) - 3)/(-2(2sin(1\u03c0x + 2) + 2) + 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(2cos(2\u03c0(-5x^2 + 1x + 1) + 1) + 1) - 1)/(-1(2cos(2\u03c0(-5x^2 + 1x + 1) + 1) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-2cos(1\u03c0(-3x^2 + 5x - 1) + 3) + 1)^2 - 2(-2cos(1\u03c0(-3x^2 + 5x - 1) + 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-3((-2x - 3)/(3x + 3))^2 + 3((-2x - 3)/(3x + 3)) + 5) + 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(-3((3x - 3)/(-1x + 2)) - 1) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(4(2cos(1\u03c0x + 3) - 2) + 5) + 1)/(-1(4(2cos(1\u03c0x + 3) - 2) + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(2(4x^2 - 4x - 4)^2 - 4(4x^2 - 4x - 4) + 2) + 3)/(2(2(4x^2 - 4x - 4)^2 - 4(4x^2 - 4x - 4) + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2|(-2cos(3\u03c0x + 3) + 1) - 3| + 1)^2 - 5(-2|(-2cos(3\u03c0x + 3) + 1) - 3| + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3(1|x|) - 4)^2 - 1(3(1|x|) - 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(2(2x^2 + 3x + 1) - 4)^2 + 1(2(2x^2 + 3x + 1) - 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(4(-1|x - 1| + 2)^2 - 4(-1|x - 1| + 2) + 4)^2 - 5(4(-1|x - 1| + 2)^2 - 4(-1|x - 1| + 2) + 4) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(5x^2 + 2x - 4) + 3)/(2(5x^2 + 2x - 4) - 1)) - 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-4(3sin(1\u03c0x - 3) - 1) - 2)^2 + 1(-4(3sin(1\u03c0x - 3) - 1) - 2) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0((3((-1x - 3)/(2x + 1)))/(-2((-1x - 3)/(2x + 1)) - 3)) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(3(-1x) + 5) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(1(4x^2 - 4x - 3)^2 - 5(4x^2 - 4x - 3) + 4)^2 - 5(1(4x^2 - 4x - 3)^2 - 5(4x^2 - 4x - 3) + 4) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(-3(-5x + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(3sin(3\u03c0(-2x + 5) - 1) + 3) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-5(-3|x - 1| + 2)) - 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|((2(-3x^2 + 2x + 1) - 2)/(-2(-3x^2 + 2x + 1) - 2)) + 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-1(-1x^2 - 4x + 5)^2 - 2(-1x^2 - 4x + 5) + 4) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(3\u03c0((3x + 1)/(2x)) + 2) - 3) + 2)/(1(3sin(3\u03c0((3x + 1)/(2x)) + 2) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2sin(2\u03c0((3x - 1)/(-2x + 3)) - 2)) + 2)/(2(-2sin(2\u03c0((3x - 1)/(-2x + 3)) - 2))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(1sin(3\u03c0(-2|x + 2|) - 2)) + 1 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": "How many solutions does the equation 5(-1(-1x^2 - 4x + 4)^2 - 5(-1x^2 - 4x + 4)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(2sin(1\u03c0(-1|x + 1| - 1)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3(3x^2 + 2x - 5) + 2)^2 - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-5(-1cos(2\u03c0x - 3) - 1)^2 - 3(-1cos(2\u03c0x - 3) - 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(1(5x^2 + 3x - 1) + 4) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1567", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1(1|x + 1| - 1)^2 + 1(1|x + 1| - 1) - 3)^2 - 2(1(1|x + 1| - 1)^2 + 1(1|x + 1| - 1) - 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(2|(-4x^2 - 3x + 2)| - 2) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(-4(-1|x + 1|)^2 + 3(-1|x + 1|) - 2) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(-1|((-3x - 2)/(-1x - 2)) + 3| + 2) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(5(5x)^2 - 4(5x) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1572", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(3|(-2|x - 1| - 3) + 3| + 3) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(1\u03c0(4((-1x + 3)/(2x - 1)) + 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-5(-1sin(1\u03c0x - 1))^2 - 3(-1sin(1\u03c0x - 1)) + 1) - 2)/(3(-5(-1sin(1\u03c0x - 1))^2 - 3(-1sin(1\u03c0x - 1)) + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-3sin(3\u03c0(1x^2 - 3x - 4) - 1) - 3) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(3(1x^2 - 5)^2 - 2(1x^2 - 5) + 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(1|(5x - 1) - 1| + 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-3cos(1\u03c0(1|x| - 1) + 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3e^(-1(5(2x^2 - 3x - 4)^2 - 4(2x^2 - 3x - 4) - 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(4(5x + 1)^2 + 1(5x + 1) - 1) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1166", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-5(-2x - 4)^2 - 4(-2x - 4) + 2)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1170", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-3|(-3|x + 1| + 3) - 1| + 2) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(3cos(3\u03c0((-2x - 2)/(2x)) + 1) + 1)^2 + 5(3cos(3\u03c0((-2x - 2)/(2x)) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-1((2x - 1)/(3x)) - 5) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(5((3x + 2)/(-2x - 1))^2 - 4((3x + 2)/(-2x - 1)) - 4)^2 + 2(5((3x + 2)/(-2x - 1))^2 - 4((3x + 2)/(-2x - 1)) - 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((-2(-2cos(2\u03c0x + 3) + 1) - 3)/(2(-2cos(2\u03c0x + 3) + 1))) - 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((1(-4x^2 + 3x))/(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": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(2cos(1\u03c0(-4x^2 - 4x - 3)) + 1) + 1)/(-2(2cos(1\u03c0(-4x^2 - 4x - 3)) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0(-2|((-2x - 1)/(2x)) + 1| - 3) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1|(3x^2 - 5x - 2) - 2|) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(2\u03c0(-1|(-5x + 5) - 1| - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(1cos(1\u03c0(2|x + 3| + 3) + 2) + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-3sin(3\u03c0(1x - 4) - 1) - 1) - 2)/(-3(-3sin(3\u03c0(1x - 4) - 1) - 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3|(2|x - 3| - 1) - 1| + 3) - 3)/(-3(-3|(2|x - 3| - 1) - 1| + 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(2\u03c0(-1(-1|x + 3| - 3) + 1) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(4(-1x^2 - 1x + 3)^2 - 1(-1x^2 - 1x + 3) - 5) + 1)/(2(4(-1x^2 - 1x + 3)^2 - 1(-1x^2 - 1x + 3) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-3(3sin(3\u03c0x + 1) - 3)^2 - 2(3sin(3\u03c0x + 1) - 3) + 2) - 2)/(-2(-3(3sin(3\u03c0x + 1) - 3)^2 - 2(3sin(3\u03c0x + 1) - 3) + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1(-3cos(3\u03c0x - 3) - 3) + 5) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-1|(-1x + 1) - 1| - 1) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(1(-1|x - 1|)^2 + 5(-1|x - 1|) + 1) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(1sin(2\u03c0(2x^2 + 1x - 3) + 3) + 1)| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(2\u03c0(-4(5x^2 - 4x - 5)^2 + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1117", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|((-2(-2sin(2\u03c0x - 2) - 3) - 3)/(2(-2sin(2\u03c0x - 2) - 3) + 2))| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-1(3sin(1\u03c0x - 1) - 2)^2 - 1(3sin(1\u03c0x - 1) - 2) + 2)^2 - 4(-1(3sin(1\u03c0x - 1) - 2)^2 - 1(3sin(1\u03c0x - 1) - 2) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(1|(2|x - 3| - 2) - 1|) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-1(1sin(2\u03c0x - 2) + 1)^2) + 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": "Determine the number of values x in [-10, 10] where f(x) = -5((-3(3sin(3\u03c0x - 3) + 3) + 3)/(-1(3sin(3\u03c0x - 3) + 3) + 2)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(4(1x^2 + 4x) - 4)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|((2(-3x^2 - 5x) - 2)/(1(-3x^2 - 5x))) + 1| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((1(-3cos(2\u03c0x) + 1) + 3)/(-2(-3cos(2\u03c0x) + 1) - 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-4(-1|x - 3| + 3)^2 - 2(-1|x - 3| + 3) + 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-5(3x^2 - 4x) + 3)^2 - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(-2(-5x^2 - 5x - 1) + 3) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1538", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(1cos(2\u03c0(-2|x - 2| - 2) + 2) + 1)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(1|(-5x - 4) - 3| + 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1(-3|x + 3|)^2 + 3(-3|x + 3|) + 5) - 3)/(-2(1(-3|x + 3|)^2 + 3(-3|x + 3|) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0((-2(3x^2 - 5x + 3) - 1)/(1(3x^2 - 5x + 3) + 2)) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(3|(3x^2 + 4x - 5) - 3| - 1) - 2)/(-2(3|(3x^2 + 4x - 5) - 3| - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(2sin(3\u03c0(1x + 1)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-3|(3x^2 + 2x + 3) - 3| + 2)| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(1(2x^2 - 4x - 3)^2 + 3(2x^2 - 4x - 3) + 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2cos(1\u03c0(2x - 2) - 1) + 2) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2((1x - 1)/(3x - 2))^2 + 3((1x - 1)/(3x - 2)) - 1)^2 - 1(2((1x - 1)/(3x - 2))^2 + 3((1x - 1)/(3x - 2)) - 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((-3(-3|x| + 2) - 3)/(-1(-3|x| + 2) + 3))^2 - 4((-3(-3|x| + 2) - 3)/(-1(-3|x| + 2) + 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(4(1|x - 3| - 3) - 4) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|((-2(3cos(3\u03c0x) - 1))/(2(3cos(3\u03c0x) - 1) + 2)) + 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((2(-1|x + 1| + 1) + 1)/(1(-1|x + 1| + 1) + 1))^2 - 5((2(-1|x + 1| + 1) + 1)/(1(-1|x + 1| + 1) + 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-5(3x^2 - 3x - 2) - 4) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((2(1|x|) + 2)/(2(1|x|) - 1)) + 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(1|(4x^2 + 3x - 3) - 1| - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(4(1|x - 1| - 1)^2 + 2(1|x - 1| - 1) - 5) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-3sin(1\u03c0((-3x + 2)/(-3x + 4))) - 1) - 2)/(-3(-3sin(1\u03c0((-3x + 2)/(-3x + 4))) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2((1(-2cos(1\u03c0x + 3)) + 1)/(-3(-2cos(1\u03c0x + 3)) - 1))^2 - 5((1(-2cos(1\u03c0x + 3)) + 1)/(-3(-2cos(1\u03c0x + 3)) - 1)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-5(2cos(1\u03c0x - 2) - 3) - 5) - 3)/(-2(-5(2cos(1\u03c0x - 2) - 3) - 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-1(-4x^2 - 1x + 5)^2 - 1(-4x^2 - 1x + 5) + 5)^2 - 1(-1(-4x^2 - 1x + 5)^2 - 1(-4x^2 - 1x + 5) + 5) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1(-3x + 5)^2 + 5(-3x + 5) - 2) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-1|(-1x + 2)| + 3)^2 + 1(-1|(-1x + 2)| + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-4(3|x + 3|)^2 - 5(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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2(5x - 2)^2 + 3(5x - 2) - 4)^2 - 4(2(5x - 2)^2 + 3(5x - 2) - 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-5(4x^2 - 1x - 3) + 1)^2 - 5(-5(4x^2 - 1x - 3) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-1(2x - 3)^2 - 5(2x - 3) - 5)^2 - 5(-1(2x - 3)^2 - 5(2x - 3) - 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(2(-2|x| + 3)^2 + 2(-2|x| + 3) - 5) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-1cos(3\u03c0((-2x + 1)/(2x + 2)) - 1) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(1((-3x - 3)/(-1x + 2))^2 + 1((-3x - 3)/(-1x + 2)) + 4) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2cos(2\u03c0((1x)/(-2x - 1)) + 1)) - 2)/(1(2cos(2\u03c0((1x)/(-2x - 1)) + 1)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0(-2(3|x - 1|)^2 + 1(3|x - 1|) - 5) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1131", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(1(5x - 4)^2 + 2(5x - 4)) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1033", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(1|((-3x + 2)/(-1x + 2)) + 1| - 1)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-1(-3cos(1\u03c0x - 2) + 1) + 5) - 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((-3(5x^2 - 3x - 5) + 1)/(-3(5x^2 - 3x - 5) + 4))^2 + 4((-3(5x^2 - 3x - 5) + 1)/(-3(5x^2 - 3x - 5) + 4)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2))^2 - 1(1(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3|(-1x^2 - 3x + 2) - 2| + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3sin(2\u03c0(1|x + 1| - 1) - 1) - 1) - 5 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 number of x-intercepts of the function f(x) = 5(3|(-2x^2 + 3x + 5) + 2| - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(5(-5x^2 - 4x + 1) + 2) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1170", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(3(2x + 1)^2 + 5(2x + 1) - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1380", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(3(-3|x + 2| - 3)^2 - 1(-3|x + 2| - 3) - 2) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1165", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-3cos(1\u03c0(1x - 4) + 2) - 1) + 2| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1((-1(3cos(1\u03c0x + 2) - 1) - 3)/(-1(3cos(1\u03c0x + 2) - 1) + 3)) - 1)/(3((-1(3cos(1\u03c0x + 2) - 1) - 3)/(-1(3cos(1\u03c0x + 2) - 1) + 3))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-3cos(3\u03c0(2x^2 + 5x - 5) + 3) + 2) + 1)/(-1(-3cos(3\u03c0(2x^2 + 5x - 5) + 3) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-5(-2sin(2\u03c0x - 1))^2 + 3(-2sin(2\u03c0x - 1)) + 3) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0(1(-2x - 1) - 5)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-2sin(2\u03c0((2x - 3)/(1x - 3)) - 2) + 3) - 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-3cos(3\u03c0(5x - 2) + 1) + 3) - 2)/(-1(-3cos(3\u03c0(5x - 2) + 1) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((2(2sin(1\u03c0x + 2) - 2))/(3(2sin(1\u03c0x + 2) - 2) + 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2(-3sin(2\u03c0x - 3) + 2)^2 - 2(-3sin(2\u03c0x - 3) + 2) + 3) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(2\u03c0(-2x + 4)) + 1) - 2)/(1(-3sin(2\u03c0(-2x + 4)) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1((-2(-2x^2 + 2x + 1) + 3)/(-2(-2x^2 + 2x + 1) + 1))^2 - 5((-2(-2x^2 + 2x + 1) + 3)/(-2(-2x^2 + 2x + 1) + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-4(-5x^2 + 3x + 1) + 4)^2 + 2(-4(-5x^2 + 3x + 1) + 4) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(2|(1x^2 + 4x + 2) - 1| - 3)^2 - 4(2|(1x^2 + 4x + 2) - 1| - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(5(-1x^2 - 4x - 1)^2 - 5(-1x^2 - 4x - 1) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-1sin(2\u03c0((-3x + 1)/(2x + 2)) - 2) - 3) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(2sin(2\u03c0(-2x + 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-3(-1sin(2\u03c0x + 3) + 2) + 3) + 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-4(1sin(3\u03c0x + 1) + 2) + 5) + 1)/(2(-4(1sin(3\u03c0x + 1) + 2) + 5) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(3(5x^2 - 5x + 2) - 4) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-2sin(1\u03c0(4x^2 + 4x - 1) - 3) + 1)^2 - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1139", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(2((2x - 1)/(-2x - 3))^2 + 4((2x - 1)/(-2x - 3)) - 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(5(1|x + 2| - 3)^2 - 2(1|x + 2| - 3) - 5) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-3(2sin(2\u03c0x) - 2) - 3)/(-2(2sin(2\u03c0x) - 2))) + 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": "Determine the number of values x in [-10, 10] where f(x) = -1(-1|(3x^2 + 5x + 1)| + 2)^2 - 4(-1|(3x^2 + 5x + 1)| + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(1cos(1\u03c0x + 2))^2 - 3(1cos(1\u03c0x + 2))) - 1)/(2(-1(1cos(1\u03c0x + 2))^2 - 3(1cos(1\u03c0x + 2)))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(4(2sin(1\u03c0x - 1) + 2)^2 + 1(2sin(1\u03c0x - 1) + 2) - 4)^2 + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1cos(2\u03c0(2|x - 1|)) - 2) - 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": "Determine the number of values x in [-10, 10] where f(x) = 2((3(1|x - 3| - 1) - 3)/(-1(1|x - 3| - 1) - 3))^2 - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1sin(2\u03c0(5x + 3) - 1) + 2) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(1|(1|x + 3| - 1) - 1| - 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-2|(5x + 5) + 3| + 3)^2 - 5(-2|(5x + 5) + 3| + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(-1(1x^2 + 3x + 2) - 5) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1|(5x^2 + 4x - 3) + 1| + 3)^2 + 3(-1|(5x^2 + 4x - 3) + 1| + 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(2cos(2\u03c0(-1x^2 + 4x + 5) + 3)) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(3\u03c0(-3(5x - 3)^2 - 2(5x - 3) - 5)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1278", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1|(-2cos(1\u03c0x) - 3) - 2| - 3) - 3)/(1(1|(-2cos(1\u03c0x) - 3) - 2| - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-3sin(2\u03c0(-3x - 2) - 1) + 2) - 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": "How many solutions does the equation 2cos(3\u03c0(-1(2|x| + 1) - 1) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3(-3|x - 2| + 3) - 2)^2 + 5(-3(-3|x - 2| + 3) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(-2(2|x + 1| + 3)^2 - 5(2|x + 1| + 3) + 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1707", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0((3(4x^2 - 4x - 5))/(3(4x^2 - 4x - 5) + 1)) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(3cos(2\u03c0(5x - 4) + 2) - 2)^2 - 3(3cos(2\u03c0(5x - 4) + 2) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(-2|(-3x + 3) + 1| - 3) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3cos(2\u03c0((-1x - 3)/(2x + 1)) + 1) - 3) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-2cos(3\u03c0((-2x - 1)/(-1x - 2)) - 2) - 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(4(3|x - 1| - 3) - 5)^2 - 5(4(3|x - 1| - 3) - 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-1(-1x^2 + 2x + 5) + 4) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(2|(1x^2 + 5x + 1) - 2| + 1) - 3| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(2|(3|x + 3| + 2) - 3| + 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(1(3sin(1\u03c0x - 2) - 3) + 3)^2 + 1(1(3sin(1\u03c0x - 2) - 3) + 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": "Determine the number of values x in [-10, 10] where f(x) = -1(-3cos(3\u03c0((-1x - 3)/(-3x)) + 3))^2 + 5(-3cos(3\u03c0((-1x - 3)/(-3x)) + 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-1cos(2\u03c0((-3x + 3)/(2x - 3)) - 3) - 2)^2 - 5(-1cos(2\u03c0((-3x + 3)/(2x - 3)) - 3) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(5(3|x + 1| - 1)^2 - 2(3|x + 1| - 1) - 1) - 1)/(3(5(3|x + 1| - 1)^2 - 2(3|x + 1| - 1) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(-5((-3x)/(-3x - 1)) - 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(5(-5x + 4) + 4)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1500", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(5(-2e^(1x) + 3)^2 + 5(-2e^(1x) + 3) - 5) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-1(2x + 4)^2 + 2(2x + 4) + 1) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0((-1(1|x - 1| + 1) + 2)/(-1(1|x - 1| + 1) - 2)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(1(-3cos(1\u03c0x + 1) + 2)^2 - 2) - 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-2cos(3\u03c0(-5x^2 + 2x - 5) - 3) + 3)^2 + 3(-2cos(3\u03c0(-5x^2 + 2x - 5) - 3) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1577", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(3sin(1\u03c0(3x + 5) - 2) - 1) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-3sin(3\u03c0((2x - 1)/(2x + 2)) - 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(3(1sin(2\u03c0x - 2))^2 - 4(1sin(2\u03c0x - 2))) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3sin(3\u03c0(2|x| + 3) - 3))^2 - 1(3sin(3\u03c0(2|x| + 3) - 3)) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-3(-3x^2 - 4x + 3) - 3)| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-5(2cos(3\u03c0x))^2 + 5(2cos(3\u03c0x)) + 2)| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-3(1x^2 + 3x - 3)^2 - 4(1x^2 + 3x - 3) + 3) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-1cos(1\u03c0(-3x^2 - 5x - 4) - 1) - 1))/(3(-1cos(1\u03c0(-3x^2 - 5x - 4) - 1) - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((1(1cos(1\u03c0x - 3) + 1) + 2)/(-2(1cos(1\u03c0x - 3) + 1) + 1))^2 - 3((1(1cos(1\u03c0x - 3) + 1) + 2)/(-2(1cos(1\u03c0x - 3) + 1) + 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}