Which is the difference between them? (besides being builtin or not). For the simple examples that I have tested, their output seems the same, eg:

`convert/function`(f,[1]);
                                 f(1)

`?()`(f,[1]);
                                 f(1)

To be "updated" I have defined in Maple 12 an "identity function" using '_passed', but the output shows 'args':

id:=()->_passed; 
                           id := () -> args

Based on the paragraph:

Prior to Maple 10, _passed and _npassed were called args and nargs. For backward compatibility, these names will continue to work as synonyms for the new names.

from ?using_parameters, I find this result unexpected. In fact, I would have expected the other way round, ie that here:

Let me call them this way. I wonder whether there is a "conversion" table between these names. Examples:

After ?invtrig:

For real arguments x, y, the two-argument function arctan(y, x), computes the principal value of the argument of the complex number x+I*y, so -Pi < arctan(y, x) <= Pi.

For any point in C or R^2 (x,y)<>(0,0) the geometrical meaning of this result is clear: the angle that the segment/vector from (0,0) to (x,y) forms with the x-axis. But this angle is undefined if this point is the origin.

So, what is arctan(0,0)?, and what it should be?

In ?property > Description it is stated:

A property can be:
...
(2) most types (this includes constant values, for example, 0)

E.g. I can do:

assume(x,1):
about(x);

Originally x, renamed x~:
  is assumed to be: 1

is(x,1);
                                    true

But, I am missing a useful example for such a property.

Besides, I find these properties confusing as 0 and 1 have parent properties entries in the property lattice, but not 2: