Ueberhuber and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical computation of a univariate integral, and "cubature" to mean numerical computation of a multiple integral. Cubature techniques available in the Wolfram Language include Monte Carlo integration, implemented as NIntegrate[f, ..., Method -> MonteCarlo] or NIntegrate[f, ..., Method -> QuasiMonteCarlo], and the adaptive Genz-Malik algorithm, implemented as NIntegrate[f, ..., Method -> MultiDimensional].
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