@MarcinM Regarding "I do not understand the philosophy of plotting vector functions in Maple", you need to go back to Stewart's chapter 13 where space curves are introduced as vector-valued functions like this:
r(t) = < f(t), g(t), h(t) >
where t is a parameter.
The Maple command spacecurve( < f(t), g(t), h(t) > , t=a..b) plots that parametric curve.
But the parameter need not be named "t". Any symbol may be used for the parameter. In the answer that I posted, the parameter is named "x", as in:
C1 := < x, sqrt(1-x^2), 0>;
As to plotting surfaces in Maple, we do
plot3d([f(x,y), g(x,y), h(x,y)], x=a..b, y=c..d);
The parametric surface here is described as a list [f, g, h], but a vector description, as in <f,g,h> works just as well and produces the same result. I used the vector representation in my answer.