My Calculus III students stumbled on this buggy thing while evaluating a line integral to calculate the flux
The curve [X(t),Y(t)] is the right-half of a Lemniscate with polar equation
The vector field is
They were integrating M*dy-N*dx around the curve.
If we let a=M*dy and aa=expand(M*dy), then they find that Maple's int gives inconsistent results.
As far as I can tell, a and its twin aa are well-behaved over -Pi/4..Pi/4 and equal. Maybe it is a bug in how Maple handles elliptic integrals? Or maybe it is some issue with removable discontinuities?
Code follows: notice how int(a,t=-Pi/4..Pi/4) and
int(aa,t=-Pi/4..Pi/4) are not equal, but ought to be equal.