NUMINT: Numerical Integration over the square: Matlab routines for computing numerical integration over the square. Tensor-product formulae based on one-dimensional Gaussian quadratures are developed for evaluating double integrals of the type indicated in the title. If the singularities occur only along the diagonal and the regular part of the integrand is a polynomial of total degree d, the formulae can be made exact by choosing the number of quadrature points larger than, or equal to, 1 + d/2. This dataset contains 20 Matlab codes and files: r_jacobi.m, r_jacobi01.m, r_jacobilog.m, r_jaclog.m, mm_log.m, mm_jacobilog.m, chebyshev.m, gauss.m, Ial.m, test_Ial.m, fxy_test.m, Ex1_Ial.m, Ex2_Istaral.m, fxy_peaks.m, Istaral.m, test_Istaral.m, c_Istaral.m, SearsKarman_Istaral.m, fxy_Sears.m, fxy_Karman.m, Dopt.m, P_matrix.m, fxy_pkpl.m, p_jacobi01.m. This serves as a companion piece to the paper Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics”,Numerical Algorithms,Oct 2012, Volume 61.