2 of 4 added 173 characters in body

Task 1, Octave, 15 bytes

@(n)(n*n-n)^2/4

Task 2, Julia, 28 bytes

n->(isprime(n)&&ispow2(n+1))

Task 5, Yacas, 45 bytes

pneumonoultramicroscopicsilicovolcanoconiosis

Task 9, Mathematica, 4 bytes

1##&