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Can I put a higher capacity battery in my mid 2009 MBP?
You can only replace the battery with the same spec battery. I wouldn't trust or recommend any non-Apple battery, due to the number of problems reported with "knockoff" batteries. Also, there is no assurance that knockoff batteries have the same charging technology that Apple uses, involving the battery, the MagSafe adapter and the Mac's logic board.

Battery Replacement
Replacing the built-in battery in your MacBook Pro
Replacing the Battery in your MacBook Air
Intel-based Apple Portables: How to replace or service a built-in battery

This should answer most, if not all, of your battery questions:
 
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