Wow, that was definitely not the direction I was anticipating this to
take...

Robert's contribution is very interesting, though I'm not sure how
indefinite integrals (without "+C") fit into that framework.

As to the issue on the tracs, my view is that an indefinite integral
is not a function in the same sense as a derivative, and that (unlike
plot and diff) there are two really fundamentally different objects
both referred to by the name "integral" (darn you, Leibniz!), so
consistency is not as useful a guide for this.

As far as I can tell, having integrate(sin(x), (x, 0, pi)) is no
problem to add, nor multiple integration in general.  The only problem
(and presumably deprecation necessity) would be whether integrate
(f,x,y,z) is a triple indefinite integral or a definite integral with
y and z as endpoints.  I've made my views known on this above :)

As a side note, it is unfortunate that Python won't (will it?) allow
integrate(f,(x),(y),(z)) to indicate the triple integral and needs the
tuple notation integrate(f,(x,),(y,),(z,)).  Of course it is easy to
allow integrate(f,[x],[y],[z]) for this, but that certainly doesn't
address the consistency question.

- kcrisman
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