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$\@$ is the function composition operator.

$\@\@$ is the repeated function composition operator.

If n is negative, the $\mathrm{invfunc}$ table is checked to see if it has an entry for f. That is, if $\mathrm{invfunc}\left[f\right]=g$, then $f\@\@n-->g\@\@\left(-n\right)$.

You can enter the composition operator @ using either the 1-D or 2-D calling sequence. For example, f @ g is equivalent to $f\circ g$. Note that the composition symbol $\circ$ is found in the Common Symbols palette.

Composition also applies to procedures. However, given two procedures f and g, the composition $f\circ g$ is of type function, not type procedure. For more information, see type/function and type/procedure .

(sin@cos)(x);

$\sin \left(\cos \left(x\right)\right)$

(sin@arcsin)(x);

$x$

sin@arcsin;

$\sin \circ \arcsin$

simplify((3));

$\left(\right)\mapsto \mathrm{args}$

sin@@0;

$\left(\right)\mapsto \mathrm{args}$

sin@@1;

$\sin$

(sin@@2)(x);

${\sin }^{\left(2\right)}\left(x\right)$

cos@@(-1);

$\arccos$

(D@@2)(ln);

$z\mapsto -\frac{1}{z^2}$

The @ and @@ operators are thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe .