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As far as I know the Evap Trap in your Air Box is there to meet some California Laws on vapor exiting out the intake after shutting down the engine. It basically is a carbon filter that captures the vapors to meet some California Air Quality regulations (according to Toyota Nation Board). It also restricts airflow into the Intake and as it gets dirty like any filter, will eventually let less and less air through effecting performance.
After reading on the Toyota Nation Avalon board that quite a few people pulled the Evap Trap Filter out. I decided to pull it out of my Avalons Air Box and I notice a big difference in power in the higher range (55MPH +) when I step on it, was actually surprised and it seems to be the consensus on the other board. The Avalon went for a State Inspection yesterday and passed without a problem so obviously it didn't effect that test. I then decided to remove it out of my IS350 and took it out for a spin, hard to tell if it made a difference but it seemed like it was a little more responsive (could be my imagination).
BASF is now making a some sort of coating for air boxes so the filter is not neccessary since it can rob the vehicle of performance.
Here is a pic of what I am talking about. The filter wasn't as dirty as it seems because it has some carbon element to it but danm it doesn't allow much air to flow through.