the present Maxima help manual has quad_qags default
value for epsrel as 1d-10.
The actual default appears to be 1d-8 based on
the following.
1. if I call quad_qags with the integrand containing
an unbound parameter, I get back a "noun form"
which lists all the default arguments, as in
(%i1) quad_qags(a*x,x,0,1);
(%o1) quad_qags(a x, x, 0, 1, epsrel = 1.0E-8, epsabs = 0.0, limit = 200)
2.if I call quad_qags with a hard enough integral, we can
see that the default and the forced 1d-8 results are the same
and do not correspond to 1d-10, as in
(%i7) g : x*abs(sin(5.5*x))$
(%i8) q1:quad_qags(g,x,0,%pi);
(%o8) [3.148686929198772, 1.8887795327771073E-8, 2583, 0]
(%i9) q2:quad_qags(g,x,0,%pi,epsrel=1d-8);
(%o9) [3.148686929198772, 1.8887795327771073E-8, 2583, 0]
(%i10) q3:quad_qags(g,x,0,%pi,epsrel=1d-10);
(%o10) [3.148686929179831, 1.5758239158003562E-10, 2835, 0]
(%i11) first(q3)-first(q2);
(%o11) - 1.8940404800105171E-11
The version 5.14 Manual had epsrel default = 1d-8.
Ted Woollett