One more thing to think about:
(%i155) assume(x>0)$
(%i156) mydefint1(abs(x),x,-1,1);
(%o156) 0
(%i157) integrate(abs(x),x,-1,1);
(%o157) 0
Some may disagree, but I think these are bugs (answer should be 1, not 0). One
cure is to substitute a gensym for the integration variable. If Maxima subsequently
does an asksign, it might ask for the sign of the gensym--the user won't know how to
answer. You could create a completely new context. If the global fact database contained
-a <x, x< a, there is the implied fact that a > 0. And this fact wouldn't be known
in the completely new context.
--Barton