Jim,
Numerical integration is a wheel that has been reinvented at
various times in Maxima. Better to use the quadpack functions
(translations from Fortran into Lisp) than romberg or quanc8
(a Newton-Cotes algorithm).
? quad
should show the list of quadpack functions.
Try quad_qags or quad_qag for general functions over a finite interval.
The integrand must evaluate to an ordinary float (not a bigfloat)
for the quadpack functions. My guess is that there would be no
greater accuracy by using bigfloats anyway; the integration error
is likely to be much larger than the round off error. Doubtless
there are special cases for which that's not true.
HTH
Robert Dodier