You made two mistakes I think.
To get the correct answer:
1) Set you calculator to radians.
2) Don't put the 2 in the bracket, in fact don't use the brackets there.
Try
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.
π/2 2 cos^{5} x dx, n = 4 0
the midpoints I calculated to be Pi/16, 3pi/16, 5pi/16, and 7pi/16.
giving this: (pi/8) ((2 cos(pi/16))^5 + (2 cos^5(3 pi/16))^5 +(2 cos^5(5 pi/6))^5+(2 cos^5(7pi/16))^5
I calculated this to be 50.2345 , which according to the system is wrong. Where did I go wrong? Thanks for any help!