Examples:

1. a := diff(z(t),t$2)
eq1 := g = a
eq2 := int(g,t) = int(a,t)
eq3 := int(lhs(eq2)+C1,t) = int(rhs(eq2),t)
eq4 := lhs(eq3)+C2 = rhs(eq3)

   

   Comment: Note that the constants of integration were added in so that the final result is correct. The constants of integration are important because you will want to specify the initial position (C2) and velocity (C1) of the object. If these are not included then the initial position is z(0)=0 and the initial velocity is z’(0)=0. So again, Maple is very smart about doing math, but it does not replace understanding the problem that you are solving.