Maple makes a strong distinction (as it should) between expressions
and functions. An expression is made up of variables, numbers, and the
standard mathematical operations of addition, subtraction,
multiplication, division, and exponentiation. For example,
is an expression, but **x=2** is not, because the equals sign is not one
of the allowed operations.

A function, on the other hand, is a more abstract object. It has a set of allowed input values and a rule for determining exactly one output value from each input values. That is, a function is an input-output machine. In practice, however, expressions are very often used to define functions, for example , but there can be functions defined without using expresssions.

The syntax for defining functions in Maple
uses the symbol ``-**>**'', made by typing the two characters - and
**>**. Using this syntax, the function is defined as
follows.

> f:= x -> x^2+1;

Functions are handled differently than expressions are in Maple. You
can evaluate the function at **x=a** with the simple command

**>**`f(a);`

You can also compose functions or define new functions in terms of
old ones. Some examples are given below. Note that the independent
variable you use to define the function is only a placeholder. That
is, if you define a function **f** using **x** as the independent
variable, Maple will cope with changing the independent variable in a
way that is mathematically correct.

> f(2);

> f(3*t);

> h := t -> sin(2*t);

> h(0);

> h(x);

> f(h(t));

> f(h(x));

Mon Aug 28 09:31:56 EDT 1995