{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0001.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{74} + \\mu_{1}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0002.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(8 y)}{y} = 8 - \\alpha_{2}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0003.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + k^2 \\psi = DERIV_117 + \\lambda_{3}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0004.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} t^{2} e^{-5 t} dt = \\frac{2}{5^{3}} + \\gamma_{4}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0005.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} t^{5} e^{-5 t} dt = \\frac{120}{5^{6}} + \\gamma_{5}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0006.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} t^{4} e^{-2 t} dt = \\frac{24}{2^{5}} + \\gamma_{6}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0007.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(8 x)}{x} = 8 - \\alpha_{7}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0008.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{8_z=0}^{N} \\frac{1}{8_z^{2}} = \\zeta(2) + \\theta_{8}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0009.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(8 t)}{t} = 8 - \\alpha_{9}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0010.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{109} + \\mu_{10}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0011.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{11_x=1}^{\\infty} \\frac{1}{11_x^{5}} = \\zeta(5) + \\theta_{11}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0012.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{12}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0013.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{13_y=1}^{\\infty} \\frac{1}{13_y^{4}} = \\zeta(4) + \\theta_{13}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0014.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} z^{5} e^{-8 z} dz = \\frac{120}{8^{6}} + \\gamma_{14}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0015.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} y^{2} e^{-7 y} dy = \\frac{2}{7^{3}} + \\gamma_{15}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0016.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} y^{3} e^{-2 y} dy = \\frac{6}{2^{4}} + \\gamma_{16}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0017.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(8 y)}{y} = 8 - \\alpha_{17}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0018.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{100} + \\mu_{18}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0019.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{19}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0020.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{20_z=0}^{N} \\frac{1}{20_z^{2}} = \\zeta(2) + \\theta_{20}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0021.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + k^2 h = DERIV_32 + \\lambda_{21}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0022.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{22}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0023.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{130} + \\mu_{23}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0024.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{24_t=1}^{\\infty} \\frac{1}{24_t^{2}} = \\zeta(2) + \\theta_{24}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0025.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{25}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0026.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{26_y=0}^{\\infty} \\frac{1}{26_y^{5}} = \\zeta(5) + \\theta_{26}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0027.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(4 t)}{t} = 4 - \\alpha_{27}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0028.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{28_y=1}^{\\infty} \\frac{1}{28_y^{3}} = \\zeta(3) + \\theta_{28}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0029.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} z^{2} e^{-2 z} dz = \\frac{2}{2^{3}} + \\gamma_{29}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0030.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{2} e^{-9 y} dy = \\frac{2}{9^{3}} + \\gamma_{30}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0031.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} y^{2} e^{-2 y} dy = \\frac{2}{2^{3}} + \\gamma_{31}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0032.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} t^{4} e^{-2 t} dt = \\frac{24}{2^{5}} + \\gamma_{32}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0033.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{33_z=0}^{N} \\frac{1}{33_z^{4}} = \\zeta(4) + \\theta_{33}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0034.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{65} + \\mu_{34}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0035.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{117} + \\mu_{35}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0036.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{36_z=1}^{N} \\frac{1}{36_z^{4}} = \\zeta(4) + \\theta_{36}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0037.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{37}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0038.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{38}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0039.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\lambda^2 h = DERIV_117 + \\lambda_{39}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0040.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{40_z=1}^{N} \\frac{1}{40_z^{2}} = \\zeta(2) + \\theta_{40}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0041.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\lambda^2 u = DERIV_80 + \\lambda_{41}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0042.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} x^{2} e^{-3 x} dx = \\frac{2}{3^{3}} + \\gamma_{42}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0043.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial z^2} + \\lambda^2 u = DERIV_72 + \\lambda_{43}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0044.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{44}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0045.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} x^{2} e^{-6 x} dx = \\frac{2}{6^{3}} + \\gamma_{45}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0046.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{46_x=1}^{N} \\frac{1}{46_x^{4}} = \\zeta(4) + \\theta_{46}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0047.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(2 x)}{x} = 2 - \\alpha_{47}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0048.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + \\beta^2 \\psi = DERIV_225 + \\lambda_{48}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0049.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} y^{5} e^{-2 y} dy = \\frac{120}{2^{6}} + \\gamma_{49}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0050.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} x^{3} e^{-7 x} dx = \\frac{6}{7^{4}} + \\gamma_{50}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0051.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(8 t)}{t} = 8 - \\alpha_{51}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0052.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} z^{3} e^{-7 z} dz = \\frac{6}{7^{4}} + \\gamma_{52}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0053.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(7 x)}{x} = 7 - \\alpha_{53}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0054.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{54_z=0}^{N} \\frac{1}{54_z^{3}} = \\zeta(3) + \\theta_{54}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0055.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{55}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0056.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\beta^2 \\psi = DERIV_32 + \\lambda_{56}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0057.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{57}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0058.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{61} + \\mu_{58}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0059.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial z^2} + \\beta^2 u = DERIV_90 + \\lambda_{59}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0060.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{72} + \\mu_{60}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0061.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(3 t)}{t} = 3 - \\alpha_{61}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0062.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{62_x=1}^{N} \\frac{1}{62_x^{4}} = \\zeta(4) + \\theta_{62}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0063.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} t^{2} e^{-6 t} dt = \\frac{2}{6^{3}} + \\gamma_{63}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0064.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(9 x)}{x} = 9 - \\alpha_{64}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0065.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{52} + \\mu_{65}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0066.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{66}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0067.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{34} + \\mu_{67}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0068.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{61} + \\mu_{68}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0069.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(7 z)}{z} = 7 - \\alpha_{69}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0070.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{70_z=1}^{N} \\frac{1}{70_z^{3}} = \\zeta(3) + \\theta_{70}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0071.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(2 x)}{x} = 2 - \\alpha_{71}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0072.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(8 t)}{t} = 8 - \\alpha_{72}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0073.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{73}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0074.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{74_x=0}^{N} \\frac{1}{74_x^{5}} = \\zeta(5) + \\theta_{74}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0075.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(6 x)}{x} = 6 - \\alpha_{75}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0076.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{76_z=0}^{N} \\frac{1}{76_z^{5}} = \\zeta(5) + \\theta_{76}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0077.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(6 y)}{y} = 6 - \\alpha_{77}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0078.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} y^{5} e^{-8 y} dy = \\frac{120}{8^{6}} + \\gamma_{78}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0079.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{117} + \\mu_{79}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0080.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{45} + \\mu_{80}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0081.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} z^{2} e^{-7 z} dz = \\frac{2}{7^{3}} + \\gamma_{81}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0082.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{82}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0083.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{83_t=1}^{N} \\frac{1}{83_t^{2}} = \\zeta(2) + \\theta_{83}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0084.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{84_t=0}^{N} \\frac{1}{84_t^{3}} = \\zeta(3) + \\theta_{84}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0085.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(8 y)}{y} = 8 - \\alpha_{85}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0086.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + \\beta^2 h = DERIV_45 + \\lambda_{86}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0087.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(8 x)}{x} = 8 - \\alpha_{87}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0088.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} y^{3} e^{-3 y} dy = \\frac{6}{3^{4}} + \\gamma_{88}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0089.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{52} + \\mu_{89}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0090.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{181} + \\mu_{90}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0091.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{106} + \\mu_{91}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0092.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\pi} x^{4} e^{-2 x} dx = \\frac{24}{2^{5}} + \\gamma_{92}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0093.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{93_x=1}^{N} \\frac{1}{93_x^{3}} = \\zeta(3) + \\theta_{93}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0094.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{74} + \\mu_{94}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0095.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} x^{4} e^{-5 x} dx = \\frac{24}{5^{5}} + \\gamma_{95}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0096.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} t^{2} e^{-6 t} dt = \\frac{2}{6^{3}} + \\gamma_{96}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0097.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} t^{2} e^{-3 t} dt = \\frac{2}{3^{3}} + \\gamma_{97}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0098.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{98}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0099.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{99_z=0}^{\\infty} \\frac{1}{99_z^{2}} = \\zeta(2) + \\theta_{99}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0100.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{130} + \\mu_{100}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0101.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{101_z=1}^{N} \\frac{1}{101_z^{3}} = \\zeta(3) + \\theta_{101}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0102.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{100} + \\mu_{102}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0103.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{100} + \\mu_{103}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0104.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} y^{2} e^{-3 y} dy = \\frac{2}{3^{3}} + \\gamma_{104}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0105.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + \\beta^2 h = DERIV_181 + \\lambda_{105}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0106.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{106}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0107.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{160} + \\mu_{107}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0108.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(5 y)}{y} = 5 - \\alpha_{108}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0109.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{109_x=0}^{N} \\frac{1}{109_x^{3}} = \\zeta(3) + \\theta_{109}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0110.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} x^{2} e^{-3 x} dx = \\frac{2}{3^{3}} + \\gamma_{110}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0111.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + k^2 \\psi = DERIV_125 + \\lambda_{111}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0112.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{112_z=1}^{N} \\frac{1}{112_z^{2}} = \\zeta(2) + \\theta_{112}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0113.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{85} + \\mu_{113}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0114.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} x^{4} e^{-7 x} dx = \\frac{24}{7^{5}} + \\gamma_{114}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0115.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(4 z)}{z} = 4 - \\alpha_{115}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0116.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{225} + \\mu_{116}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0117.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{136} + \\mu_{117}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0118.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{b} x^{5} e^{-7 x} dx = \\frac{120}{7^{6}} + \\gamma_{118}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0119.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\pi} y^{4} e^{-6 y} dy = \\frac{24}{6^{5}} + \\gamma_{119}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0120.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{120}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0121.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + k^2 h = DERIV_117 + \\lambda_{121}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0122.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{97} + \\mu_{122}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0123.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{61} + \\mu_{123}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0124.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(6 y)}{y} = 6 - \\alpha_{124}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0125.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{125_x=0}^{\\infty} \\frac{1}{125_x^{3}} = \\zeta(3) + \\theta_{125}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0126.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{202} + \\mu_{126}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0127.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} z^{3} e^{-6 z} dz = \\frac{6}{6^{4}} + \\gamma_{127}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0128.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} t^{4} e^{-3 t} dt = \\frac{24}{3^{5}} + \\gamma_{128}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0129.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(6 y)}{y} = 6 - \\alpha_{129}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0130.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{130}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0131.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{160} + \\mu_{131}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0132.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} z^{4} e^{-5 z} dz = \\frac{24}{5^{5}} + \\gamma_{132}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0133.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + \\lambda^2 \\Phi = DERIV_41 + \\lambda_{133}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0134.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{208} + \\mu_{134}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0135.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{145} + \\mu_{135}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0136.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{145} + \\mu_{136}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0137.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{137}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0138.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{138_z=1}^{\\infty} \\frac{1}{138_z^{3}} = \\zeta(3) + \\theta_{138}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0139.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{b} t^{3} e^{-6 t} dt = \\frac{6}{6^{4}} + \\gamma_{139}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0140.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{140_z=1}^{\\infty} \\frac{1}{140_z^{5}} = \\zeta(5) + \\theta_{140}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0141.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} t^{5} e^{-5 t} dt = \\frac{120}{5^{6}} + \\gamma_{141}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0142.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(5 t)}{t} = 5 - \\alpha_{142}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0143.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{61} + \\mu_{143}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0144.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{5} e^{-4 y} dy = \\frac{120}{4^{6}} + \\gamma_{144}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0145.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{89} + \\mu_{145}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0146.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + \\beta^2 \\psi = DERIV_181 + \\lambda_{146}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0147.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(7 x)}{x} = 7 - \\alpha_{147}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0148.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{148_t=0}^{\\infty} \\frac{1}{148_t^{3}} = \\zeta(3) + \\theta_{148}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0149.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} z^{2} e^{-2 z} dz = \\frac{2}{2^{3}} + \\gamma_{149}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0150.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{150_x=0}^{N} \\frac{1}{150_x^{4}} = \\zeta(4) + \\theta_{150}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0151.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} x^{5} e^{-3 x} dx = \\frac{120}{3^{6}} + \\gamma_{151}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0152.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} x^{4} e^{-9 x} dx = \\frac{24}{9^{5}} + \\gamma_{152}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0153.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\lambda^2 \\Phi = DERIV_74 + \\lambda_{153}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0154.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{157} + \\mu_{154}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0155.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + k^2 u = DERIV_89 + \\lambda_{155}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0156.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{156_t=1}^{\\infty} \\frac{1}{156_t^{3}} = \\zeta(3) + \\theta_{156}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0157.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{157}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0158.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{208} + \\mu_{158}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0159.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{159_z=0}^{\\infty} \\frac{1}{159_z^{2}} = \\zeta(2) + \\theta_{159}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0160.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + k^2 h = DERIV_109 + \\lambda_{160}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0161.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} x^{5} e^{-2 x} dx = \\frac{120}{2^{6}} + \\gamma_{161}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0162.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{162}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0163.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{163_t=1}^{\\infty} \\frac{1}{163_t^{3}} = \\zeta(3) + \\theta_{163}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0164.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} z^{2} e^{-5 z} dz = \\frac{2}{5^{3}} + \\gamma_{164}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0165.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{109} + \\mu_{165}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0166.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{25} + \\mu_{166}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0167.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{2} e^{-3 y} dy = \\frac{2}{3^{3}} + \\gamma_{167}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0168.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\beta^2 \\psi = DERIV_106 + \\lambda_{168}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0169.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_58 + \\lambda_{169}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0170.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(8 y)}{y} = 8 - \\alpha_{170}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0171.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{171_t=1}^{\\infty} \\frac{1}{171_t^{3}} = \\zeta(3) + \\theta_{171}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0172.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{65} + \\mu_{172}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0173.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} y^{5} e^{-4 y} dy = \\frac{120}{4^{6}} + \\gamma_{173}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0174.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{174_t=1}^{N} \\frac{1}{174_t^{5}} = \\zeta(5) + \\theta_{174}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0175.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{175}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0176.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + \\beta^2 h = DERIV_106 + \\lambda_{176}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0177.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{136} + \\mu_{177}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0178.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(5 z)}{z} = 5 - \\alpha_{178}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0179.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{113} + \\mu_{179}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0180.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + k^2 h = DERIV_116 + \\lambda_{180}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0181.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{181}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0182.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} z^{4} e^{-3 z} dz = \\frac{24}{3^{5}} + \\gamma_{182}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0183.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + \\beta^2 h = DERIV_80 + \\lambda_{183}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0184.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_162 + \\lambda_{184}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0185.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{113} + \\mu_{185}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0186.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} x^{5} e^{-7 x} dx = \\frac{120}{7^{6}} + \\gamma_{186}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0187.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_162 + \\lambda_{187}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0188.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{58} + \\mu_{188}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0189.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} y^{3} e^{-6 y} dy = \\frac{6}{6^{4}} + \\gamma_{189}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0190.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{145} + \\mu_{190}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0191.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{58} + \\mu_{191}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0192.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{80} + \\mu_{192}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0193.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{193_y=0}^{N} \\frac{1}{193_y^{5}} = \\zeta(5) + \\theta_{193}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0194.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(7 z)}{z} = 7 - \\alpha_{194}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0195.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} t^{4} e^{-5 t} dt = \\frac{24}{5^{5}} + \\gamma_{195}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0196.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} t^{2} e^{-4 t} dt = \\frac{2}{4^{3}} + \\gamma_{196}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0197.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} z^{2} e^{-5 z} dz = \\frac{2}{5^{3}} + \\gamma_{197}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0198.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} z^{3} e^{-8 z} dz = \\frac{6}{8^{4}} + \\gamma_{198}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0199.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(2 t)}{t} = 2 - \\alpha_{199}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0200.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{125} + \\mu_{200}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0201.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{65} + \\mu_{201}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0202.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{208} + \\mu_{202}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0203.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{203}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0204.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(3 t)}{t} = 3 - \\alpha_{204}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0205.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{205_y=1}^{N} \\frac{1}{205_y^{3}} = \\zeta(3) + \\theta_{205}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0206.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{206_t=1}^{N} \\frac{1}{206_t^{3}} = \\zeta(3) + \\theta_{206}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0207.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{116} + \\mu_{207}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0208.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\beta^2 \\psi = DERIV_225 + \\lambda_{208}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0209.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} y^{5} e^{-7 y} dy = \\frac{120}{7^{6}} + \\gamma_{209}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0210.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{210_x=1}^{N} \\frac{1}{210_x^{5}} = \\zeta(5) + \\theta_{210}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0211.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(7 z)}{z} = 7 - \\alpha_{211}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0212.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{212_t=1}^{\\infty} \\frac{1}{212_t^{3}} = \\zeta(3) + \\theta_{212}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0213.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + \\lambda^2 \\Phi = DERIV_130 + \\lambda_{213}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0214.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{214_t=1}^{N} \\frac{1}{214_t^{3}} = \\zeta(3) + \\theta_{214}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0215.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + \\lambda^2 h = DERIV_137 + \\lambda_{215}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0216.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} t^{5} e^{-4 t} dt = \\frac{120}{4^{6}} + \\gamma_{216}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0217.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(5 t)}{t} = 5 - \\alpha_{217}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0218.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} y^{4} e^{-7 y} dy = \\frac{24}{7^{5}} + \\gamma_{218}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0219.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{52} + \\mu_{219}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0220.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{34} + \\mu_{220}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0221.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{221}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0222.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{208} + \\mu_{222}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0223.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} x^{2} e^{-3 x} dx = \\frac{2}{3^{3}} + \\gamma_{223}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0224.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{100} + \\mu_{224}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0225.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(6 y)}{y} = 6 - \\alpha_{225}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0226.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{226}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0227.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{97} + \\mu_{227}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0228.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_181 + \\lambda_{228}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0229.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + \\lambda^2 u = DERIV_41 + \\lambda_{229}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0230.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{61} + \\mu_{230}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0231.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{231_z=0}^{N} \\frac{1}{231_z^{5}} = \\zeta(5) + \\theta_{231}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0232.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{232_x=0}^{\\infty} \\frac{1}{232_x^{4}} = \\zeta(4) + \\theta_{232}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0233.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{233_t=1}^{\\infty} \\frac{1}{233_t^{3}} = \\zeta(3) + \\theta_{233}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0234.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{234_t=0}^{N} \\frac{1}{234_t^{5}} = \\zeta(5) + \\theta_{234}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0235.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(9 x)}{x} = 9 - \\alpha_{235}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0236.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\lambda^2 h = DERIV_74 + \\lambda_{236}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0237.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{237_z=0}^{N} \\frac{1}{237_z^{2}} = \\zeta(2) + \\theta_{237}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0238.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{238_x=0}^{N} \\frac{1}{238_x^{2}} = \\zeta(2) + \\theta_{238}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0239.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{239}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0240.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + \\lambda^2 \\psi = DERIV_85 + \\lambda_{240}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0241.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + k^2 \\psi = DERIV_160 + \\lambda_{241}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0242.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{242_t=0}^{\\infty} \\frac{1}{242_t^{3}} = \\zeta(3) + \\theta_{242}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0243.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{243_x=1}^{N} \\frac{1}{243_x^{2}} = \\zeta(2) + \\theta_{243}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0244.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} t^{4} e^{-4 t} dt = \\frac{24}{4^{5}} + \\gamma_{244}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0245.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{65} + \\mu_{245}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0246.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\lambda^2 u = DERIV_25 + \\lambda_{246}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0247.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\beta^2 \\psi = DERIV_180 + \\lambda_{247}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0248.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{248}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0249.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_137 + \\lambda_{249}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0250.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + \\beta^2 \\psi = DERIV_117 + \\lambda_{250}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0251.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{130} + \\mu_{251}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0252.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{252}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0253.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} y^{4} e^{-9 y} dy = \\frac{24}{9^{5}} + \\gamma_{253}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0254.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} y^{5} e^{-2 y} dy = \\frac{120}{2^{6}} + \\gamma_{254}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0255.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + \\beta^2 \\Phi = DERIV_85 + \\lambda_{255}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0256.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{128} + \\mu_{256}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0257.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{257_z=0}^{\\infty} \\frac{1}{257_z^{3}} = \\zeta(3) + \\theta_{257}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0258.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{258_t=1}^{\\infty} \\frac{1}{258_t^{3}} = \\zeta(3) + \\theta_{258}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0259.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} x^{3} e^{-6 x} dx = \\frac{6}{6^{4}} + \\gamma_{259}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0260.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} x^{4} e^{-3 x} dx = \\frac{24}{3^{5}} + \\gamma_{260}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0261.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{261_z=1}^{N} \\frac{1}{261_z^{5}} = \\zeta(5) + \\theta_{261}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0262.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{262_z=1}^{N} \\frac{1}{262_z^{3}} = \\zeta(3) + \\theta_{262}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0263.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{263_x=0}^{\\infty} \\frac{1}{263_x^{2}} = \\zeta(2) + \\theta_{263}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0264.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{264_x=0}^{\\infty} \\frac{1}{264_x^{4}} = \\zeta(4) + \\theta_{264}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0265.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{265_t=1}^{N} \\frac{1}{265_t^{3}} = \\zeta(3) + \\theta_{265}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0266.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{25} + \\mu_{266}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0267.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{162} + \\mu_{267}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0268.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{268_x=1}^{\\infty} \\frac{1}{268_x^{3}} = \\zeta(3) + \\theta_{268}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0269.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(8 x)}{x} = 8 - \\alpha_{269}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0270.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} z^{4} e^{-6 z} dz = \\frac{24}{6^{5}} + \\gamma_{270}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0271.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{89} + \\mu_{271}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0272.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{272}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0273.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{273}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0274.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(8 x)}{x} = 8 - \\alpha_{274}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0275.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{275_t=0}^{N} \\frac{1}{275_t^{4}} = \\zeta(4) + \\theta_{275}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0276.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{74} + \\mu_{276}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0277.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{277_y=0}^{\\infty} \\frac{1}{277_y^{3}} = \\zeta(3) + \\theta_{277}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0278.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{278_t=0}^{\\infty} \\frac{1}{278_t^{4}} = \\zeta(4) + \\theta_{278}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0279.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} y^{5} e^{-3 y} dy = \\frac{120}{3^{6}} + \\gamma_{279}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0280.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial x^2} + \\beta^2 \\Phi = DERIV_202 + \\lambda_{280}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0281.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{281_y=1}^{\\infty} \\frac{1}{281_y^{2}} = \\zeta(2) + \\theta_{281}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0282.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} t^{5} e^{-9 t} dt = \\frac{120}{9^{6}} + \\gamma_{282}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0283.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{85} + \\mu_{283}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0284.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + k^2 \\psi = DERIV_130 + \\lambda_{284}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0285.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(7 z)}{z} = 7 - \\alpha_{285}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0286.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{74} + \\mu_{286}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0287.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + k^2 h = DERIV_130 + \\lambda_{287}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0288.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{162} + \\mu_{288}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0289.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{89} + \\mu_{289}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0290.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} x^{2} e^{-8 x} dx = \\frac{2}{8^{3}} + \\gamma_{290}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0291.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} t^{4} e^{-7 t} dt = \\frac{24}{7^{5}} + \\gamma_{291}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0292.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + k^2 u = DERIV_185 + \\lambda_{292}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0293.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} y^{2} e^{-5 y} dy = \\frac{2}{5^{3}} + \\gamma_{293}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0294.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_169 + \\lambda_{294}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0295.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} x^{3} e^{-5 x} dx = \\frac{6}{5^{4}} + \\gamma_{295}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0296.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{225} + \\mu_{296}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0297.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} y^{5} e^{-8 y} dy = \\frac{120}{8^{6}} + \\gamma_{297}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0298.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{149} + \\mu_{298}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0299.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(7 x)}{x} = 7 - \\alpha_{299}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0300.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{193} + \\mu_{300}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0301.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{301}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0302.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{65} + \\mu_{302}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0303.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\lambda^2 \\Phi = DERIV_137 + \\lambda_{303}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0304.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{304_y=0}^{\\infty} \\frac{1}{304_y^{2}} = \\zeta(2) + \\theta_{304}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0305.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{305_z=1}^{\\infty} \\frac{1}{305_z^{4}} = \\zeta(4) + \\theta_{305}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0306.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{52} + \\mu_{306}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0307.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{307}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0308.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{308_z=1}^{\\infty} \\frac{1}{308_z^{5}} = \\zeta(5) + \\theta_{308}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0309.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{309_y=1}^{\\infty} \\frac{1}{309_y^{4}} = \\zeta(4) + \\theta_{309}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0310.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + k^2 \\Phi = DERIV_52 + \\lambda_{310}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0311.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(6 y)}{y} = 6 - \\alpha_{311}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0312.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{312_z=0}^{\\infty} \\frac{1}{312_z^{2}} = \\zeta(2) + \\theta_{312}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0313.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{313_t=0}^{N} \\frac{1}{313_t^{2}} = \\zeta(2) + \\theta_{313}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0314.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{113} + \\mu_{314}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0315.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} y^{4} e^{-3 y} dy = \\frac{24}{3^{5}} + \\gamma_{315}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0316.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{170} + \\mu_{316}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0317.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{34} + \\mu_{317}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0318.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + k^2 \\Phi = DERIV_109 + \\lambda_{318}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0319.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} x^{4} e^{-4 x} dx = \\frac{24}{4^{5}} + \\gamma_{319}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0320.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{32} + \\mu_{320}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0321.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{321_z=0}^{N} \\frac{1}{321_z^{5}} = \\zeta(5) + \\theta_{321}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0322.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\lambda^2 \\Phi = DERIV_117 + \\lambda_{322}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0323.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{145} + \\mu_{323}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0324.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} y^{3} e^{-7 y} dy = \\frac{6}{7^{4}} + \\gamma_{324}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0325.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{325}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0326.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} t^{3} e^{-3 t} dt = \\frac{6}{3^{4}} + \\gamma_{326}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0327.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{327_x=1}^{\\infty} \\frac{1}{327_x^{3}} = \\zeta(3) + \\theta_{327}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0328.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{149} + \\mu_{328}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0329.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{329}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0330.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\beta^2 u = DERIV_25 + \\lambda_{330}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0331.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{130} + \\mu_{331}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0332.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{332_y=1}^{\\infty} \\frac{1}{332_y^{2}} = \\zeta(2) + \\theta_{332}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0333.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\beta^2 h = DERIV_73 + \\lambda_{333}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0334.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(2 t)}{t} = 2 - \\alpha_{334}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0335.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{335_z=1}^{\\infty} \\frac{1}{335_z^{4}} = \\zeta(4) + \\theta_{335}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0336.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{97} + \\mu_{336}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0337.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\lambda^2 \\psi = DERIV_25 + \\lambda_{337}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0338.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} z^{4} e^{-5 z} dz = \\frac{24}{5^{5}} + \\gamma_{338}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0339.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{339}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0340.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + \\lambda^2 u = DERIV_169 + \\lambda_{340}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0341.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(5 z)}{z} = 5 - \\alpha_{341}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0342.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} t^{5} e^{-2 t} dt = \\frac{120}{2^{6}} + \\gamma_{342}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0343.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(4 t)}{t} = 4 - \\alpha_{343}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0344.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(7 z)}{z} = 7 - \\alpha_{344}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0345.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{345}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0346.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\beta^2 \\Phi = DERIV_45 + \\lambda_{346}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0347.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{347}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0348.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} x^{5} e^{-7 x} dx = \\frac{120}{7^{6}} + \\gamma_{348}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0349.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(7 x)}{x} = 7 - \\alpha_{349}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0350.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{350_z=0}^{N} \\frac{1}{350_z^{5}} = \\zeta(5) + \\theta_{350}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0351.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{351}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0352.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{65} + \\mu_{352}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0353.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\lambda^2 \\psi = DERIV_125 + \\lambda_{353}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0354.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} z^{3} e^{-6 z} dz = \\frac{6}{6^{4}} + \\gamma_{354}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0355.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\beta^2 \\Phi = DERIV_137 + \\lambda_{355}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0356.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{157} + \\mu_{356}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0357.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + k^2 h = DERIV_73 + \\lambda_{357}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0358.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} y^{2} e^{-5 y} dy = \\frac{2}{5^{3}} + \\gamma_{358}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0359.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{193} + \\mu_{359}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0360.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{360_x=1}^{N} \\frac{1}{360_x^{2}} = \\zeta(2) + \\theta_{360}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0361.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{361_z=0}^{\\infty} \\frac{1}{361_z^{4}} = \\zeta(4) + \\theta_{361}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0362.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{362}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0363.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} z^{3} e^{-5 z} dz = \\frac{6}{5^{4}} + \\gamma_{363}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0364.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{364}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0365.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{116} + \\mu_{365}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0366.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{366}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0367.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} z^{2} e^{-2 z} dz = \\frac{2}{2^{3}} + \\gamma_{367}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0368.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\lambda^2 h = DERIV_164 + \\lambda_{368}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0369.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{97} + \\mu_{369}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0370.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\beta^2 h = DERIV_89 + \\lambda_{370}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0371.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{371}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0372.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{74} + \\mu_{372}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0373.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{373}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0374.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{374_z=0}^{N} \\frac{1}{374_z^{4}} = \\zeta(4) + \\theta_{374}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0375.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_157 + \\lambda_{375}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0376.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{106} + \\mu_{376}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0377.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{377_y=0}^{\\infty} \\frac{1}{377_y^{4}} = \\zeta(4) + \\theta_{377}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0378.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} t^{2} e^{-9 t} dt = \\frac{2}{9^{3}} + \\gamma_{378}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0379.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{379}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0380.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_181 + \\lambda_{380}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0381.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{381_z=1}^{\\infty} \\frac{1}{381_z^{3}} = \\zeta(3) + \\theta_{381}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0382.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(2 t)}{t} = 2 - \\alpha_{382}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0383.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(6 x)}{x} = 6 - \\alpha_{383}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0384.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{384_x=1}^{\\infty} \\frac{1}{384_x^{3}} = \\zeta(3) + \\theta_{384}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0385.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{385_y=1}^{\\infty} \\frac{1}{385_y^{3}} = \\zeta(3) + \\theta_{385}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0386.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + k^2 u = DERIV_72 + \\lambda_{386}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0387.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{387}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0388.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{145} + \\mu_{388}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0389.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{106} + \\mu_{389}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0390.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{50} + \\mu_{390}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0391.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{162} + \\mu_{391}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0392.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{392_x=0}^{\\infty} \\frac{1}{392_x^{4}} = \\zeta(4) + \\theta_{392}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0393.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + k^2 \\psi = DERIV_98 + \\lambda_{393}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0394.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{394}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0395.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} t^{2} e^{-8 t} dt = \\frac{2}{8^{3}} + \\gamma_{395}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0396.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{117} + \\mu_{396}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0397.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_52 + \\lambda_{397}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0398.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{398_z=0}^{N} \\frac{1}{398_z^{4}} = \\zeta(4) + \\theta_{398}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0399.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{399_x=0}^{\\infty} \\frac{1}{399_x^{3}} = \\zeta(3) + \\theta_{399}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0400.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{130} + \\mu_{400}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0401.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{65} + \\mu_{401}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0402.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{145} + \\mu_{402}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0403.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{137} + \\mu_{403}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0404.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(9 x)}{x} = 9 - \\alpha_{404}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0405.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + \\beta^2 \\Phi = DERIV_180 + \\lambda_{405}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0406.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} t^{2} e^{-3 t} dt = \\frac{2}{3^{3}} + \\gamma_{406}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0407.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{116} + \\mu_{407}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0408.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} x^{5} e^{-3 x} dx = \\frac{120}{3^{6}} + \\gamma_{408}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0409.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\pi} x^{5} e^{-5 x} dx = \\frac{120}{5^{6}} + \\gamma_{409}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0410.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{410_y=1}^{N} \\frac{1}{410_y^{5}} = \\zeta(5) + \\theta_{410}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0411.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{65} + \\mu_{411}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0412.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_128 + \\lambda_{412}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0413.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_74 + \\lambda_{413}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0414.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} t^{5} e^{-4 t} dt = \\frac{120}{4^{6}} + \\gamma_{414}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0415.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{415_z=1}^{N} \\frac{1}{415_z^{3}} = \\zeta(3) + \\theta_{415}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0416.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\beta^2 u = DERIV_116 + \\lambda_{416}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0417.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} z^{2} e^{-2 z} dz = \\frac{2}{2^{3}} + \\gamma_{417}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0418.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{418_y=1}^{N} \\frac{1}{418_y^{5}} = \\zeta(5) + \\theta_{418}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0419.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} z^{4} e^{-2 z} dz = \\frac{24}{2^{5}} + \\gamma_{419}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0420.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\beta^2 u = DERIV_117 + \\lambda_{420}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0421.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{421}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0422.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\lambda^2 \\psi = DERIV_181 + \\lambda_{422}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0423.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{423}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0424.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{424_y=1}^{\\infty} \\frac{1}{424_y^{5}} = \\zeta(5) + \\theta_{424}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0425.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + k^2 u = DERIV_97 + \\lambda_{425}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0426.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{128} + \\mu_{426}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0427.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} t^{5} e^{-7 t} dt = \\frac{120}{7^{6}} + \\gamma_{427}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0428.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{428}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0429.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{145} + \\mu_{429}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0430.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(8 y)}{y} = 8 - \\alpha_{430}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0431.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{431_y=0}^{\\infty} \\frac{1}{431_y^{4}} = \\zeta(4) + \\theta_{431}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0432.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\lambda^2 \\psi = DERIV_185 + \\lambda_{432}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0433.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{433}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0434.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} z^{4} e^{-4 z} dz = \\frac{24}{4^{5}} + \\gamma_{434}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0435.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + k^2 \\psi = DERIV_181 + \\lambda_{435}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0436.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + \\beta^2 h = DERIV_225 + \\lambda_{436}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0437.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{437}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0438.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + \\lambda^2 h = DERIV_65 + \\lambda_{438}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0439.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{439}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0440.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} z^{3} e^{-5 z} dz = \\frac{6}{5^{4}} + \\gamma_{440}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0441.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{441}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0442.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{202} + \\mu_{442}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0443.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{443}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0444.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial z^2} + \\lambda^2 u = DERIV_97 + \\lambda_{444}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0445.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\beta^2 h = DERIV_73 + \\lambda_{445}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0446.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{446_z=1}^{\\infty} \\frac{1}{446_z^{2}} = \\zeta(2) + \\theta_{446}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0447.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{80} + \\mu_{447}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0448.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\beta^2 \\psi = DERIV_225 + \\lambda_{448}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0449.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{449_t=0}^{\\infty} \\frac{1}{449_t^{5}} = \\zeta(5) + \\theta_{449}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0450.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{25} + \\mu_{450}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0451.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} t^{3} e^{-7 t} dt = \\frac{6}{7^{4}} + \\gamma_{451}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0452.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{452_z=0}^{N} \\frac{1}{452_z^{3}} = \\zeta(3) + \\theta_{452}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0453.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{34} + \\mu_{453}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0454.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + \\lambda^2 \\psi = DERIV_58 + \\lambda_{454}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0455.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{455_y=1}^{N} \\frac{1}{455_y^{2}} = \\zeta(2) + \\theta_{455}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0456.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + k^2 \\psi = DERIV_65 + \\lambda_{456}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0457.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} y^{3} e^{-5 y} dy = \\frac{6}{5^{4}} + \\gamma_{457}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0458.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_80 + \\lambda_{458}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0459.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{459}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0460.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{225} + \\mu_{460}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0461.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{117} + \\mu_{461}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0462.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + k^2 u = DERIV_181 + \\lambda_{462}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0463.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} y^{3} e^{-8 y} dy = \\frac{6}{8^{4}} + \\gamma_{463}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0464.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + k^2 u = DERIV_100 + \\lambda_{464}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0465.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{465_t=1}^{\\infty} \\frac{1}{465_t^{3}} = \\zeta(3) + \\theta_{465}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0466.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{466_y=1}^{N} \\frac{1}{466_y^{5}} = \\zeta(5) + \\theta_{466}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0467.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\lambda^2 \\Phi = DERIV_72 + \\lambda_{467}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0468.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{468_t=1}^{\\infty} \\frac{1}{468_t^{2}} = \\zeta(2) + \\theta_{468}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0469.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} y^{3} e^{-3 y} dy = \\frac{6}{3^{4}} + \\gamma_{469}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0470.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{169} + \\mu_{470}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0471.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{471_z=0}^{N} \\frac{1}{471_z^{2}} = \\zeta(2) + \\theta_{471}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0472.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{74} + \\mu_{472}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0473.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(7 x)}{x} = 7 - \\alpha_{473}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0474.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{474_t=1}^{\\infty} \\frac{1}{474_t^{3}} = \\zeta(3) + \\theta_{474}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0475.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} y^{2} e^{-7 y} dy = \\frac{2}{7^{3}} + \\gamma_{475}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0476.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{113} + \\mu_{476}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0477.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\lambda^2 u = DERIV_41 + \\lambda_{477}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0478.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(2 t)}{t} = 2 - \\alpha_{478}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0479.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{479_x=1}^{\\infty} \\frac{1}{479_x^{3}} = \\zeta(3) + \\theta_{479}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0480.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{480}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0481.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + k^2 \\Phi = DERIV_125 + \\lambda_{481}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0482.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} y^{5} e^{-5 y} dy = \\frac{120}{5^{6}} + \\gamma_{482}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0483.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + k^2 u = DERIV_89 + \\lambda_{483}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0484.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{484_x=0}^{N} \\frac{1}{484_x^{3}} = \\zeta(3) + \\theta_{484}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0485.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{80} + \\mu_{485}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0486.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{486}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0487.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{487}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0488.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{488}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0489.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} x^{5} e^{-6 x} dx = \\frac{120}{6^{6}} + \\gamma_{489}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0490.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{490}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0491.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(5 y)}{y} = 5 - \\alpha_{491}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0492.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} y^{4} e^{-3 y} dy = \\frac{24}{3^{5}} + \\gamma_{492}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0493.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{493}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0494.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{130} + \\mu_{494}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0495.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{495}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0496.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + \\lambda^2 \\psi = DERIV_85 + \\lambda_{496}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0497.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} t^{4} e^{-7 t} dt = \\frac{24}{7^{5}} + \\gamma_{497}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0498.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} y^{5} e^{-9 y} dy = \\frac{120}{9^{6}} + \\gamma_{498}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0499.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial x^2} + k^2 \\Phi = DERIV_146 + \\lambda_{499}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0500.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{500_x=1}^{N} \\frac{1}{500_x^{2}} = \\zeta(2) + \\theta_{500}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0501.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + \\lambda^2 \\psi = DERIV_90 + \\lambda_{501}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0502.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} y^{4} e^{-5 y} dy = \\frac{24}{5^{5}} + \\gamma_{502}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0503.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} x^{2} e^{-2 x} dx = \\frac{2}{2^{3}} + \\gamma_{503}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0504.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{504_t=1}^{\\infty} \\frac{1}{504_t^{2}} = \\zeta(2) + \\theta_{504}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0505.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\lambda^2 \\Phi = DERIV_73 + \\lambda_{505}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0506.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{506_t=1}^{N} \\frac{1}{506_t^{5}} = \\zeta(5) + \\theta_{506}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0507.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{507}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0508.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} t^{2} e^{-8 t} dt = \\frac{2}{8^{3}} + \\gamma_{508}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0509.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_58 + \\lambda_{509}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0510.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{510_y=0}^{\\infty} \\frac{1}{510_y^{4}} = \\zeta(4) + \\theta_{510}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0511.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{511}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0512.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{153} + \\mu_{512}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0513.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(6 x)}{x} = 6 - \\alpha_{513}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0514.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{89} + \\mu_{514}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0515.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(5 y)}{y} = 5 - \\alpha_{515}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0516.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{516_t=0}^{N} \\frac{1}{516_t^{2}} = \\zeta(2) + \\theta_{516}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0517.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{128} + \\mu_{517}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0518.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_74 + \\lambda_{518}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0519.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + k^2 \\Phi = DERIV_72 + \\lambda_{519}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0520.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{98} + \\mu_{520}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0521.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(4 t)}{t} = 4 - \\alpha_{521}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0522.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} x^{5} e^{-6 x} dx = \\frac{120}{6^{6}} + \\gamma_{522}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0523.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\lambda^2 \\Phi = DERIV_137 + \\lambda_{523}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0524.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(4 x)}{x} = 4 - \\alpha_{524}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0525.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + k^2 \\psi = DERIV_202 + \\lambda_{525}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0526.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{97} + \\mu_{526}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0527.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + \\beta^2 u = DERIV_164 + \\lambda_{527}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0528.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + \\lambda^2 h = DERIV_80 + \\lambda_{528}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0529.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{529_x=1}^{N} \\frac{1}{529_x^{3}} = \\zeta(3) + \\theta_{529}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0530.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{2} e^{-2 y} dy = \\frac{2}{2^{3}} + \\gamma_{530}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0531.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} x^{4} e^{-5 x} dx = \\frac{24}{5^{5}} + \\gamma_{531}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0532.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} t^{3} e^{-6 t} dt = \\frac{6}{6^{4}} + \\gamma_{532}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0533.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{74} + \\mu_{533}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0534.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{534}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0535.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} y^{5} e^{-8 y} dy = \\frac{120}{8^{6}} + \\gamma_{535}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0536.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{61} + \\mu_{536}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0537.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{73} + \\mu_{537}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0538.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{538}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0539.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{539_y=1}^{\\infty} \\frac{1}{539_y^{4}} = \\zeta(4) + \\theta_{539}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0540.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{98} + \\mu_{540}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0541.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(4 x)}{x} = 4 - \\alpha_{541}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0542.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + \\beta^2 \\Phi = DERIV_97 + \\lambda_{542}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0543.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(6 z)}{z} = 6 - \\alpha_{543}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0544.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} z^{5} e^{-2 z} dz = \\frac{120}{2^{6}} + \\gamma_{544}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0545.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{545}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0546.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{546_y=1}^{\\infty} \\frac{1}{546_y^{4}} = \\zeta(4) + \\theta_{546}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0547.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{41} + \\mu_{547}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0548.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + k^2 u = DERIV_153 + \\lambda_{548}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0549.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{549_x=1}^{\\infty} \\frac{1}{549_x^{4}} = \\zeta(4) + \\theta_{549}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0550.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{550_x=1}^{\\infty} \\frac{1}{550_x^{2}} = \\zeta(2) + \\theta_{550}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0551.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{32} + \\mu_{551}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0552.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{52} + \\mu_{552}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0553.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{73} + \\mu_{553}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0554.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{b} t^{2} e^{-4 t} dt = \\frac{2}{4^{3}} + \\gamma_{554}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0555.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(2 t)}{t} = 2 - \\alpha_{555}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0556.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(4 z)}{z} = 4 - \\alpha_{556}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0557.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{557}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0558.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{106} + \\mu_{558}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0559.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{559_t=0}^{N} \\frac{1}{559_t^{3}} = \\zeta(3) + \\theta_{559}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0560.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{560}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0561.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{561_z=1}^{\\infty} \\frac{1}{561_z^{3}} = \\zeta(3) + \\theta_{561}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0562.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{562_z=0}^{N} \\frac{1}{562_z^{2}} = \\zeta(2) + \\theta_{562}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0563.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(6 y)}{y} = 6 - \\alpha_{563}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0564.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(9 x)}{x} = 9 - \\alpha_{564}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0565.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(8 t)}{t} = 8 - \\alpha_{565}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0566.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{72} + \\mu_{566}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0567.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{41} + \\mu_{567}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0568.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{568_t=1}^{N} \\frac{1}{568_t^{5}} = \\zeta(5) + \\theta_{568}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0569.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(4 x)}{x} = 4 - \\alpha_{569}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0570.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(2 t)}{t} = 2 - \\alpha_{570}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0571.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{571_y=1}^{N} \\frac{1}{571_y^{3}} = \\zeta(3) + \\theta_{571}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0572.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{160} + \\mu_{572}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0573.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{117} + \\mu_{573}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0574.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{113} + \\mu_{574}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0575.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + k^2 \\psi = DERIV_32 + \\lambda_{575}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0576.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{74} + \\mu_{576}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0577.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + k^2 u = DERIV_98 + \\lambda_{577}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0578.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + k^2 \\Phi = DERIV_97 + \\lambda_{578}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0579.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(6 z)}{z} = 6 - \\alpha_{579}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0580.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{225} + \\mu_{580}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0581.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_100 + \\lambda_{581}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0582.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + k^2 \\psi = DERIV_50 + \\lambda_{582}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0583.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{583_t=1}^{\\infty} \\frac{1}{583_t^{3}} = \\zeta(3) + \\theta_{583}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0584.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} y^{5} e^{-5 y} dy = \\frac{120}{5^{6}} + \\gamma_{584}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0585.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + \\lambda^2 h = DERIV_180 + \\lambda_{585}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0586.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{586_t=0}^{\\infty} \\frac{1}{586_t^{2}} = \\zeta(2) + \\theta_{586}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0587.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{587_y=0}^{\\infty} \\frac{1}{587_y^{3}} = \\zeta(3) + \\theta_{587}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0588.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} z^{5} e^{-4 z} dz = \\frac{120}{4^{6}} + \\gamma_{588}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0589.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{589_x=0}^{\\infty} \\frac{1}{589_x^{4}} = \\zeta(4) + \\theta_{589}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0590.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{590_z=1}^{\\infty} \\frac{1}{590_z^{2}} = \\zeta(2) + \\theta_{590}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0591.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{591_y=1}^{\\infty} \\frac{1}{591_y^{2}} = \\zeta(2) + \\theta_{591}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0592.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{592}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0593.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{74} + \\mu_{593}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0594.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\beta^2 u = DERIV_145 + \\lambda_{594}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0595.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{157} + \\mu_{595}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0596.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{106} + \\mu_{596}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0597.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{597}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0598.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(9 x)}{x} = 9 - \\alpha_{598}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0599.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(4 x)}{x} = 4 - \\alpha_{599}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0600.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{32} + \\mu_{600}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0601.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{225} + \\mu_{601}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0602.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\lambda^2 \\psi = DERIV_74 + \\lambda_{602}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0603.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\lambda^2 \\psi = DERIV_50 + \\lambda_{603}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0604.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{181} + \\mu_{604}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0605.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{605}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0606.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{164} + \\mu_{606}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0607.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + \\beta^2 u = DERIV_74 + \\lambda_{607}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0608.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{608_z=0}^{N} \\frac{1}{608_z^{5}} = \\zeta(5) + \\theta_{608}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0609.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{609_x=0}^{N} \\frac{1}{609_x^{4}} = \\zeta(4) + \\theta_{609}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0610.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(6 x)}{x} = 6 - \\alpha_{610}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0611.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{109} + \\mu_{611}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0612.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{612_t=0}^{N} \\frac{1}{612_t^{3}} = \\zeta(3) + \\theta_{612}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0613.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} z^{4} e^{-3 z} dz = \\frac{24}{3^{5}} + \\gamma_{613}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0614.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + \\beta^2 h = DERIV_106 + \\lambda_{614}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0615.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{113} + \\mu_{615}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0616.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{616_t=1}^{N} \\frac{1}{616_t^{3}} = \\zeta(3) + \\theta_{616}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0617.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{5} e^{-5 y} dy = \\frac{120}{5^{6}} + \\gamma_{617}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0618.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} y^{4} e^{-6 y} dy = \\frac{24}{6^{5}} + \\gamma_{618}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0619.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} x^{3} e^{-3 x} dx = \\frac{6}{3^{4}} + \\gamma_{619}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0620.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{34} + \\mu_{620}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0621.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\lambda^2 \\psi = DERIV_225 + \\lambda_{621}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0622.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} y^{3} e^{-2 y} dy = \\frac{6}{2^{4}} + \\gamma_{622}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0623.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} t^{4} e^{-3 t} dt = \\frac{24}{3^{5}} + \\gamma_{623}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0624.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{624}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0625.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(4 t)}{t} = 4 - \\alpha_{625}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0626.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + k^2 u = DERIV_208 + \\lambda_{626}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0627.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\pi} y^{5} e^{-5 y} dy = \\frac{120}{5^{6}} + \\gamma_{627}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0628.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{628_z=0}^{N} \\frac{1}{628_z^{5}} = \\zeta(5) + \\theta_{628}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0629.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} x^{4} e^{-8 x} dx = \\frac{24}{8^{5}} + \\gamma_{629}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0630.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(5 z)}{z} = 5 - \\alpha_{630}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0631.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + \\lambda^2 u = DERIV_113 + \\lambda_{631}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0632.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\beta^2 h = DERIV_34 + \\lambda_{632}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0633.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{633}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0634.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{634_z=0}^{\\infty} \\frac{1}{634_z^{4}} = \\zeta(4) + \\theta_{634}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0635.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{635_y=1}^{N} \\frac{1}{635_y^{4}} = \\zeta(4) + \\theta_{635}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0636.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{636}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0637.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} x^{4} e^{-9 x} dx = \\frac{24}{9^{5}} + \\gamma_{637}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0638.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{638_x=0}^{N} \\frac{1}{638_x^{4}} = \\zeta(4) + \\theta_{638}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0639.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(5 z)}{z} = 5 - \\alpha_{639}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0640.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{640}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0641.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\beta^2 \\psi = DERIV_208 + \\lambda_{641}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0642.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(8 t)}{t} = 8 - \\alpha_{642}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0643.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(5 x)}{x} = 5 - \\alpha_{643}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0644.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_61 + \\lambda_{644}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0645.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\pi} t^{4} e^{-2 t} dt = \\frac{24}{2^{5}} + \\gamma_{645}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0646.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{157} + \\mu_{646}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0647.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{4} e^{-5 y} dy = \\frac{24}{5^{5}} + \\gamma_{647}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0648.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{149} + \\mu_{648}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0649.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(5 t)}{t} = 5 - \\alpha_{649}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0650.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{650_z=1}^{N} \\frac{1}{650_z^{4}} = \\zeta(4) + \\theta_{650}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0651.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{651_t=1}^{\\infty} \\frac{1}{651_t^{2}} = \\zeta(2) + \\theta_{651}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0652.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} t^{5} e^{-6 t} dt = \\frac{120}{6^{6}} + \\gamma_{652}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0653.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{98} + \\mu_{653}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0654.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{145} + \\mu_{654}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0655.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{130} + \\mu_{655}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0656.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} y^{2} e^{-4 y} dy = \\frac{2}{4^{3}} + \\gamma_{656}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0657.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} z^{5} e^{-2 z} dz = \\frac{120}{2^{6}} + \\gamma_{657}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0658.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{97} + \\mu_{658}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0659.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + k^2 u = DERIV_74 + \\lambda_{659}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0660.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial x^2} + \\beta^2 \\Phi = DERIV_90 + \\lambda_{660}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0661.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(8 x)}{x} = 8 - \\alpha_{661}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0662.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{208} + \\mu_{662}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0663.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{5} e^{-6 y} dy = \\frac{120}{6^{6}} + \\gamma_{663}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0664.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{664_x=1}^{N} \\frac{1}{664_x^{4}} = \\zeta(4) + \\theta_{664}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0665.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{185} + \\mu_{665}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0666.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial x^2} + k^2 \\Phi = DERIV_50 + \\lambda_{666}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0667.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{667_z=0}^{N} \\frac{1}{667_z^{4}} = \\zeta(4) + \\theta_{667}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0668.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + k^2 \\psi = DERIV_208 + \\lambda_{668}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0669.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(7 z)}{z} = 7 - \\alpha_{669}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0670.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{670}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0671.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(2 x)}{x} = 2 - \\alpha_{671}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0672.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(2 x)}{x} = 2 - \\alpha_{672}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0673.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{673}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0674.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(8 z)}{z} = 8 - \\alpha_{674}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0675.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{113} + \\mu_{675}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0676.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{146} + \\mu_{676}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0677.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\pi} x^{5} e^{-6 x} dx = \\frac{120}{6^{6}} + \\gamma_{677}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0678.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{80} + \\mu_{678}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0679.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\beta^2 \\Phi = DERIV_106 + \\lambda_{679}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0680.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(4 t)}{t} = 4 - \\alpha_{680}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0681.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{80} + \\mu_{681}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0682.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{90} + \\mu_{682}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0683.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial y^2} + \\lambda^2 \\psi = DERIV_185 + \\lambda_{683}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0684.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{61} + \\mu_{684}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0685.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{685_y=0}^{\\infty} \\frac{1}{685_y^{2}} = \\zeta(2) + \\theta_{685}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0686.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{169} + \\mu_{686}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0687.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_106 + \\lambda_{687}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0688.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(3 x)}{x} = 3 - \\alpha_{688}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0689.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{689}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0690.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\lambda^2 \\psi = DERIV_185 + \\lambda_{690}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0691.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{691_x=0}^{N} \\frac{1}{691_x^{4}} = \\zeta(4) + \\theta_{691}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0692.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{225} + \\mu_{692}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0693.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{693_x=0}^{\\infty} \\frac{1}{693_x^{5}} = \\zeta(5) + \\theta_{693}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0694.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{694}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0695.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(6 x)}{x} = 6 - \\alpha_{695}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0696.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{50} + \\mu_{696}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0697.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{32} + \\mu_{697}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0698.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(5 y)}{y} = 5 - \\alpha_{698}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0699.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} y^{5} e^{-4 y} dy = \\frac{120}{4^{6}} + \\gamma_{699}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0700.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(7 y)}{y} = 7 - \\alpha_{700}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0701.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{701_x=1}^{\\infty} \\frac{1}{701_x^{4}} = \\zeta(4) + \\theta_{701}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0702.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(5 x)}{x} = 5 - \\alpha_{702}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0703.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} x^{5} e^{-5 x} dx = \\frac{120}{5^{6}} + \\gamma_{703}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0704.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{704_t=1}^{\\infty} \\frac{1}{704_t^{3}} = \\zeta(3) + \\theta_{704}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0705.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(3 z)}{z} = 3 - \\alpha_{705}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0706.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + \\beta^2 u = DERIV_125 + \\lambda_{706}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0707.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} z^{5} e^{-2 z} dz = \\frac{120}{2^{6}} + \\gamma_{707}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0708.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{137} + \\mu_{708}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0709.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{225} + \\mu_{709}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0710.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{b} z^{5} e^{-2 z} dz = \\frac{120}{2^{6}} + \\gamma_{710}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0711.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{711_z=1}^{N} \\frac{1}{711_z^{4}} = \\zeta(4) + \\theta_{711}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0712.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{1} t^{3} e^{-2 t} dt = \\frac{6}{2^{4}} + \\gamma_{712}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0713.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(2 x)}{x} = 2 - \\alpha_{713}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0714.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} y^{3} e^{-8 y} dy = \\frac{6}{8^{4}} + \\gamma_{714}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0715.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{715_z=0}^{\\infty} \\frac{1}{715_z^{3}} = \\zeta(3) + \\theta_{715}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0716.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial x^2} + k^2 h = DERIV_100 + \\lambda_{716}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0717.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} t^{5} e^{-2 t} dt = \\frac{120}{2^{6}} + \\gamma_{717}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0718.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + k^2 \\psi = DERIV_90 + \\lambda_{718}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0719.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(5 z)}{z} = 5 - \\alpha_{719}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0720.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} z^{5} e^{-6 z} dz = \\frac{120}{6^{6}} + \\gamma_{720}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0721.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{225} + \\mu_{721}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0722.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{722_t=0}^{\\infty} \\frac{1}{722_t^{3}} = \\zeta(3) + \\theta_{722}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0723.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_61 + \\lambda_{723}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0724.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{146} + \\mu_{724}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0725.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + k^2 \\psi = DERIV_130 + \\lambda_{725}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0726.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{164} + \\mu_{726}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0727.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + \\lambda^2 u = DERIV_61 + \\lambda_{727}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0728.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{728}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0729.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{729_x=1}^{\\infty} \\frac{1}{729_x^{5}} = \\zeta(5) + \\theta_{729}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0730.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{730_t=1}^{\\infty} \\frac{1}{730_t^{3}} = \\zeta(3) + \\theta_{730}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0731.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{b} t^{4} e^{-3 t} dt = \\frac{24}{3^{5}} + \\gamma_{731}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0732.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{45} + \\mu_{732}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0733.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{733_y=1}^{N} \\frac{1}{733_y^{5}} = \\zeta(5) + \\theta_{733}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0734.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + \\beta^2 u = DERIV_117 + \\lambda_{734}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0735.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\infty} x^{2} e^{-8 x} dx = \\frac{2}{8^{3}} + \\gamma_{735}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0736.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + k^2 \\Phi = DERIV_153 + \\lambda_{736}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0737.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(8 x)}{x} = 8 - \\alpha_{737}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0738.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(4 z)}{z} = 4 - \\alpha_{738}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0739.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{1} y^{3} e^{-8 y} dy = \\frac{6}{8^{4}} + \\gamma_{739}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0740.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{740_y=1}^{N} \\frac{1}{740_y^{4}} = \\zeta(4) + \\theta_{740}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0741.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} t^{2} e^{-9 t} dt = \\frac{2}{9^{3}} + \\gamma_{741}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0742.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{100} + \\mu_{742}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0743.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(3 t)}{t} = 3 - \\alpha_{743}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0744.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{744}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0745.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{52} + \\mu_{745}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0746.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial y^2} + \\lambda^2 u = DERIV_170 + \\lambda_{746}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0747.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{73} + \\mu_{747}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0748.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(9 z)}{z} = 9 - \\alpha_{748}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0749.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial x^2} + k^2 u = DERIV_106 + \\lambda_{749}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0750.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} t^{4} e^{-3 t} dt = \\frac{24}{3^{5}} + \\gamma_{750}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0751.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial x^2} + \\lambda^2 \\Phi = DERIV_170 + \\lambda_{751}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0752.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{752}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0753.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial z^2} + \\lambda^2 u = DERIV_113 + \\lambda_{753}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0754.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{754_y=1}^{N} \\frac{1}{754_y^{5}} = \\zeta(5) + \\theta_{754}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0755.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + k^2 h = DERIV_113 + \\lambda_{755}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0756.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{756_z=1}^{N} \\frac{1}{756_z^{3}} = \\zeta(3) + \\theta_{756}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0757.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{157} + \\mu_{757}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0758.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{106} + \\mu_{758}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0759.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} x^{4} e^{-3 x} dx = \\frac{24}{3^{5}} + \\gamma_{759}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0760.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(4 y)}{y} = 4 - \\alpha_{760}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0761.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\pi}^{\\pi} x^{2} e^{-6 x} dx = \\frac{2}{6^{3}} + \\gamma_{761}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0762.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{762_y=1}^{\\infty} \\frac{1}{762_y^{2}} = \\zeta(2) + \\theta_{762}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0763.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{763}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0764.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial t^2} + k^2 \\Phi = DERIV_61 + \\lambda_{764}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0765.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{1} x^{4} e^{-4 x} dx = \\frac{24}{4^{5}} + \\gamma_{765}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0766.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial z^2} + \\beta^2 u = DERIV_136 + \\lambda_{766}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0767.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{767_z=0}^{\\infty} \\frac{1}{767_z^{4}} = \\zeta(4) + \\theta_{767}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0768.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_113 + \\lambda_{768}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0769.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + \\beta^2 h = DERIV_85 + \\lambda_{769}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0770.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} z^{4} e^{-8 z} dz = \\frac{24}{8^{5}} + \\gamma_{770}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0771.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(2 z)}{z} = 2 - \\alpha_{771}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0772.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{74} + \\mu_{772}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0773.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{773_x=1}^{\\infty} \\frac{1}{773_x^{5}} = \\zeta(5) + \\theta_{773}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0774.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{774_z=0}^{N} \\frac{1}{774_z^{2}} = \\zeta(2) + \\theta_{774}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0775.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{b} x^{5} e^{-3 x} dx = \\frac{120}{3^{6}} + \\gamma_{775}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0776.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\lambda^2 \\psi = DERIV_128 + \\lambda_{776}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0777.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + k^2 \\Phi = DERIV_90 + \\lambda_{777}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0778.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{778}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0779.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{779_y=1}^{\\infty} \\frac{1}{779_y^{5}} = \\zeta(5) + \\theta_{779}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0780.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{225} + \\mu_{780}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0781.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{781}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0782.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(9 t)}{t} = 9 - \\alpha_{782}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0783.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{783_y=0}^{N} \\frac{1}{783_y^{2}} = \\zeta(2) + \\theta_{783}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0784.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{784}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0785.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\beta^2 h = DERIV_109 + \\lambda_{785}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0786.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\beta^2 h = DERIV_128 + \\lambda_{786}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0787.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{787}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0788.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{788_y=1}^{\\infty} \\frac{1}{788_y^{5}} = \\zeta(5) + \\theta_{788}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0789.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial t^2} + \\beta^2 \\psi = DERIV_169 + \\lambda_{789}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0790.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{790_t=0}^{\\infty} \\frac{1}{790_t^{4}} = \\zeta(4) + \\theta_{790}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0791.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{170} + \\mu_{791}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0792.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + \\beta^2 \\psi = DERIV_41 + \\lambda_{792}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0793.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(9 y)}{y} = 9 - \\alpha_{793}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0794.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\infty} y^{4} e^{-2 y} dy = \\frac{24}{2^{5}} + \\gamma_{794}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0795.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(4 x)}{x} = 4 - \\alpha_{795}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0796.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{x1^2 + x2^2} = \\sqrt{50} + \\mu_{796}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0797.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + \\lambda^2 u = DERIV_225 + \\lambda_{797}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0798.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{90} + \\mu_{798}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0799.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\infty} x^{4} e^{-9 x} dx = \\frac{24}{9^{5}} + \\gamma_{799}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0800.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(2 y)}{y} = 2 - \\alpha_{800}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0801.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{89} + \\mu_{801}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0802.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(4 x)}{x} = 4 - \\alpha_{802}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0803.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{803_y=1}^{N} \\frac{1}{803_y^{2}} = \\zeta(2) + \\theta_{803}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0804.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{804_x=1}^{N} \\frac{1}{804_x^{4}} = \\zeta(4) + \\theta_{804}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0805.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\lambda^2 \\psi = DERIV_136 + \\lambda_{805}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0806.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{x \\to 0} \\frac{\\sin(9 x)}{x} = 9 - \\alpha_{806}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0807.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\lambda^2 \\Phi = DERIV_160 + \\lambda_{807}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0808.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{98} + \\mu_{808}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0809.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{90} + \\mu_{809}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0810.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{85} + \\mu_{810}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0811.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} t^{5} e^{-7 t} dt = \\frac{120}{7^{6}} + \\gamma_{811}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0812.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{812_y=0}^{N} \\frac{1}{812_y^{2}} = \\zeta(2) + \\theta_{812}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0813.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(8 t)}{t} = 8 - \\alpha_{813}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0814.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{814_z=0}^{N} \\frac{1}{814_z^{2}} = \\zeta(2) + \\theta_{814}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0815.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} y^{4} e^{-8 y} dy = \\frac{24}{8^{5}} + \\gamma_{815}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0816.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(5 t)}{t} = 5 - \\alpha_{816}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0817.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\lambda^2 \\Phi = DERIV_193 + \\lambda_{817}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0818.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{73} + \\mu_{818}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0819.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial t^2} + \\beta^2 h = DERIV_202 + \\lambda_{819}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0820.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{y \\to 0} \\frac{\\sin(3 y)}{y} = 3 - \\alpha_{820}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0821.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{50} + \\mu_{821}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0822.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{153} + \\mu_{822}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0823.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(6 t)}{t} = 6 - \\alpha_{823}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0824.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{\\pi} y^{2} e^{-6 y} dy = \\frac{2}{6^{3}} + \\gamma_{824}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0825.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{825_t=0}^{N} \\frac{1}{825_t^{4}} = \\zeta(4) + \\theta_{825}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0826.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{\\pi} t^{4} e^{-5 t} dt = \\frac{24}{5^{5}} + \\gamma_{826}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0827.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{109} + \\mu_{827}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0828.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial z^2} + k^2 u = DERIV_193 + \\lambda_{828}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0829.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_145 + \\lambda_{829}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0830.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{z1^2 + z2^2} = \\sqrt{130} + \\mu_{830}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0831.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial x^2} + k^2 \\psi = DERIV_106 + \\lambda_{831}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0832.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial y^2} + \\lambda^2 \\Phi = DERIV_137 + \\lambda_{832}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0833.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{y1^2 + y2^2} = \\sqrt{117} + \\mu_{833}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0834.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(5 z)}{z} = 5 - \\alpha_{834}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0835.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial z^2} + \\lambda^2 h = DERIV_106 + \\lambda_{835}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0836.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 h}{\\partial y^2} + \\lambda^2 h = DERIV_149 + \\lambda_{836}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0837.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\beta^2 \\psi = DERIV_85 + \\lambda_{837}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0838.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 u}{\\partial t^2} + \\lambda^2 u = DERIV_52 + \\lambda_{838}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0839.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\Phi}{\\partial z^2} + \\beta^2 \\Phi = DERIV_137 + \\lambda_{839}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0840.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{z \\to 0} \\frac{\\sin(6 z)}{z} = 6 - \\alpha_{840}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0841.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sqrt{t1^2 + t2^2} = \\sqrt{34} + \\mu_{841}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0842.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{a}^{\\infty} x^{2} e^{-3 x} dx = \\frac{2}{3^{3}} + \\gamma_{842}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0843.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + k^2 \\psi = DERIV_85 + \\lambda_{843}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0844.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(7 t)}{t} = 7 - \\alpha_{844}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0845.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{-\\infty}^{1} z^{3} e^{-7 z} dz = \\frac{6}{7^{4}} + \\gamma_{845}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0846.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\sum_{846_x=0}^{\\infty} \\frac{1}{846_x^{3}} = \\zeta(3) + \\theta_{846}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0847.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\int_{0}^{b} z^{5} e^{-7 z} dz = \\frac{120}{7^{6}} + \\gamma_{847}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0848.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\frac{\\partial^2 \\psi}{\\partial z^2} + \\beta^2 \\psi = DERIV_58 + \\lambda_{848}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0849.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(5 t)}{t} = 5 - \\alpha_{849}"}
{"pdf_filename": "bench_data/pdfs/arxiv_math/arxiv_math_0850.pdf", "page_number": 1, "test_type": "math_formula", "formula": "\\lim_{t \\to 0} \\frac{\\sin(5 t)}{t} = 5 - \\alpha_{850}"}