A student in my class can get very far in Sage without needing to
declare variables....

sage: f(u) = u^2
sage: f(4)
16
sage: integrate(sin(u),u,2,11)
cos(2) - cos(11)
sage: diff(u*y,u)
y
sage: def g(n):
....:     return n*n
....:
sage: g(9)
81

When must you absolutely need to declare vars?  My examples above give
the impression you can avoid declaring them for a good long time.

CS
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