MySQL save results of EXECUTE in a variable?

If you want to do this with a prepared statement, then you need to include the variable assignment in the original statement declaration.

If you want to use a stored routine it's easier. You can assign the return value of a stored function directly to a variable, and stored procedures support out parameters.

Examples:

Prepared Statement:

PREPARE square_stmt from 'select pow(?,2) into @outvar';
set @invar = 1;
execute square_stmt using @invar;
select @outvar;
+---------+
| @outvar |
+---------+
|       1 |
+---------+
DEALLOCATE PREPARE square_stmt;

Stored Function:

delimiter $$
create function square_func(p_input int) returns int
begin
  return pow(p_input,2);
end $$
delimiter ;

set @outvar = square_func(2);
select @outvar;
+---------+
| @outvar |
+---------+
|       4 |
+---------+

Stored Procedure:

delimiter $$
create procedure square_proc(p_input int, p_output int)
begin
  set p_output = pow(p_input,2);
end $$
delimiter ;

set @outvar = square_func(3);
call square_proc(2,@outvar);
select @outvar;
+---------+
| @outvar |
+---------+
|       9 |
+---------+