Earlier this year I reached an impasse with Maple's numerical integration package over the need for a high-resolution (say 50 or more digits) evaluation of multiple integrals for a Bayesian statistics application. An integral such as sqrt(1.+4.852800000000*chi^1411+5.887416960000*chi^200+4.852800000000*chi^100+5.887416960000*chi^2822-21.48043392000*chi^100*chi^1411) over a rectangular range like chi=0..0.9999,chi=0..0.9999999 would return unevaluated. Infolevel[`evalf/int`] explained that the methods available in Maple would not return the required precision. But the problem persisted even when I swallowed my pride and settled for 12 digits of precision. Stuck as I am, I haven't even tried to present the problem to Maple in higher dimensions.