Int((cos(t)^n+sin(t)^n)^(1/2),t = 0 ... Pi)

For
Int((cos(t)^n+sin(t)^n)^(1/2),t = 0 ... Pi)
that is
Integrate[Sqrt[Cos[t]^n + Sin[t]^n], {t, 0, Pi}]

1) n=4
Maple gives
EllipticE(I)*sqrt(2)
vs
Mathemtica's
2*EllipticE[1/2]

and
2) n=6
Maple gives
?EllipticE(sqrt(3)*I)
vs
Mathematica's
?2 EllipticE[3/4]

In both cases above Maple has explicit ?reference to the ?imaginary
part I and Mathematica doesn't ...

What Maxima does on that ?

Thanks,