I am assuming quad_qags will return a noun
form when the integrand has an interior
singularity. The expected behavior occurs
if the upper limit is 1, but not when the
upper limit is 0.999999999999
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Maxima 5.28.0-2 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
(%i1) quad_qags(x/(1/2 -x)^3,x,0,1);
(%o1) quad_qags(x/(1/2-x)^3,x,0,1,epsrel = 1.0E-8,epsabs = 0.0,limit = 200)
(%i2) quad_qags(x/(1/2 -x)^3,x,0,0.999999999999);
(%o2) [-5506.971211820142,0.0,63,0]
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Ted Woollett