I'm not quite sure, if this is the correct place but i think i found a bug in the analytic integration tool in Maple.
Since i have the student edition and i didn't find a bug report form i will post it here:
intfAna:=int(f,x= -Pi + theta .. Pi+ theta);
intfNum:=Int(f,x= -Pi + theta .. Pi+ theta);
the last two statements yield:
intNum := -0.07343950362
intAna := -0.7853981635
Thus the numerical integrated value differes from the analytical result.
Since I also tried to integrate this with scipy in python I'm pretty sure that the numerical result is correct and the analytical one is not.
Is my deduction here correct?
I have Maple 2018 here on my private PC. But at work i have Maple 2021 and the difference is the same.
Interestingly the analytic result seems to be -cos(theta)^2/4. If we plot the analytical and numerical integrand, we get:
Thus both integrands seem to be cosines of theta but the analytical has the wrong factor.
Thanks in advance!