Your derivative indicator, dt, is only meaningful if t is continuous. If your T(t) term indicates indexing, then your t needs to be discrete positive integers.
If you were to modify the expression to
Fo = integral of 10^((T*t-Tr)/z)*dt over t = 0 to time
[since a(b) might mean a*(b) which would normally be written a*b unless b is an expression] then you have two difficulties: that T is a vector, and that time is a vector.
Perhaps you want to define,
Fo(k) = integral of 10^((T(k)-Tr)/z)*dt over t = 0 to time(k)
where in that line (k) indicates indexing at offset k.
If that is what you want, then the answer becomes trivial:
Fo(k) = 10^((T(k)-Tr)/z) * time(k)
since in that circumstance 10^((T(k)-Tr)/z) would simply be a constant for the purposes of integration.
For the second part of your question about an output that is too long, we would need to see code.
