Is there any easy way to use logical "operatives"(not sure what they are called)?

e.g., x^2[x=3] = if x = 3 then 3^2 or 0

f(x)[g(x)=x^2] = f(x) when g(x)=x^2

or whatever. I don't care about the syntax but would like it to be short and distinct. There are obviously ways to get the same behavior but they are too verbose. I like the bracket syntax but I doubt maple works with it. It could be done with a binary operator that does the comparison and returns if true...

But curious if maple has such a thing built in?

Maple gave Lie algebras of a system of PDE in which some of them do not leave the system invariant. Dont know whether the mistake is maple's or mine. File attached.

Maple_2016_bug_or...mw

I have an arc length parametrization problem. I got the right answer for the speed. The lines of code before the long dividing line I successfully got to work. The main problem I am having is with the code underneath that. It is producing weird answers and just returning the same words without computing any mathematical calculation.

with(VectorCalculus):

with(plots):

T:= 4:

r := t -> <t^2 + t, sin(t^2)*(t + 1), cos(t^2)*(t + 1)>;

speed := Norm(diff(r(t), t));

evalf(Int(speed, t = 0 .. T)); (I got 62.98633182 for this part)

----------------------------This is where I started running into problems with the arc length parametrization.

L := b -> int(speed, t = 0 .. b);

speed := t -> subs(c = t, Norm(diff(r(c), c)));

speed2 := t -> sqrt(factor(simplify(speed(t)^2)));

solve(s = L(t), s);

assume(b > 0 'real');

g := s -> solve(s = L(b), b, useassumptions = true);

newr := s -> r(g(s));

newr(s);

I like to see this solution step by step. I used DiffTutor before, is there something similar for implicit differentials?

I want to find dz:

z*t = cos(z + t)

I am trying to enter an ODE into Maple and I remember that Dr. Lopez showed how to use a prime to denote differentiation. When I try I get conflicting results: if I type

>  y''+y'+3*y=0;;

Error, unexpected single forward quote
But if I copy that command from the Help page Maple understands what I want. What is going on?

BTW, there is no entry for Differential Equations on the Help page.
 

In Maple outputs, long fraction bars occur quite frequently. A common example is of the type A(x)/x, where A(x) may be a complicated expression made up by standard functions, derivatives, integrals etc. in terms of x and some constants, denoted by names. Maple displays such an expression in terms of a long solidus and x as the denominator. This looks rather weird. A preferable display would be of the form x^-1 A(x) or A(x) multiplied by 1/x. I have unsuccessfully tried to achieve this but failed. Can this be done?