this is the title of a paper that I found quite interesting, and you
might too, if you are familiar with the topic.
It now in SIAM review, but also appears online.

it's by Nick Trefethen. There are slides from a talk are located at.

http://www.comlab.ox.ac.uk/people/nick.trefethen/cctalk.pdf

The paper is at

http://portal.acm.org/citation.cfm?id=1350631

or at
ftp://ftp/comlab.ox.ac.uk a PostScript file named NA-06-07.ps

If you are not familiar with the controversy, but are curious about
how one might determine
the "best" way of doing numerical integration, you might find the
paper interesting.
(If Gaussian is supposed to be optimal and superior to Clenshaw-
Curtis, why are they nearly the same?)

Why sci.math.symbolic? These methods can work with arbitrary
precision floats.
The programs themselves can be set up in just a few lines of a CAS.
(or even Matlab, but then you have fixed precision).