Okay, thank you for this summary. Actually, already writing Pi instead of pi solved the problem, but I guess it's better to comply with all the rules.

I guess, this issue is solved then! Thank you, Kitonum and Axel Vogt!

Okay, sorry for that. As you can imagine, I'm totally new to Maple and use it almost for the first time at all.

The lower case pi did not seem to be bad, in the output Maple returned the greek letter pi in the expression for the integration limit. But as I inserted the uppercase Pi now, maple solved the integral, so I guess the greek letter pi was just meant to be some unknown? :D

Just for completeness, here is the text (is it okay in this form?):

B:=cos²(x)sqrt(1-1/4(3sin²(x)cos²(y)+cos²(x)))

evalf(Int(B,x=0..7Pi/18,y=0..2*Pi))

Thank you very much!