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You should be more careful about "expressions" and "functions".

An expression is something like this

ex = u*cos(v)

A function is something like this

cool(u,v) = u+v

One possible way to go : use only functions, and call them with arguments always :

good(u, v) = cool(u, v) + u - v

Your "right_curve_u" is an expression. Make it a function.