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.
1) Are you sure about N here? N is not defined anywhere so Mathcad assumes you mean the unit Newton. I guess this is not what you intended, as you don't use any units in the rest of your sheet.
2) The argument "a" is never used in the function definition, so Psi is not dependent on "a" and therefore the argument "a" should be omitted, use only Psi(z):=...
E(a): This function does not depend on "a". "a" is never used other than as argument of Psi and its without effect there as said above. So the result of E() is not influenced by "a" and therefore, as Mike had noticed, is the same constant value for any argument provided.
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