You haven't defined N, so Mathcad thinks it means Newtons. Your definition of Psi has 'a' as an input argument, but the right-hand side of the function doesn't contain 'a' at all (should it be alpha?)! No wonder E(a) gives a single value whatever value is passed to it for 'a'!
Psi also doesn't cater for the situation where z is exactly L/2.
Alan