Let 
be a set of expressions representing real, single-valued partially defined functions
of one real variable. Let 
be the set of functions represented by expressions in 
, where 
contains the identity function
and the rational numbers as constant functions and that 
is closed under addition, multiplication, and composition.
If 
is an expression in 
,
then let 
be the function denoted by 
.
Then the integration problem for 
is the problem of deciding, given 
in 
, whether there is a function 
in 
so that 
(Richardson 1968).
