Hey I can finally see your pictures in that last post although they are very small.
BTW where are you located because your engine bay looks nothing like any 2003 Corolla I have seen unless I am tripping.
It apears that the filter element is IN the engine bay. Therefore it is not a cold air intake.
With a cold air intake, the piping goes into the hole where your airbox used to connect to your resonator in your wheel well (which has to be removed) and the filter is located INSIDE the wheel well, hence it takes cold air from outside, rather than hot engine bay air.
Also the MAF adapter on there looks like it was welded on with a butter knife.
Here is the CAI on my 2001 Corolla to give you a basic idea:
Any performance shop should be able to weld a nipple on the intake tube for a small fee.