Most digital cameras have a rather limited flash.
I guess they do that to increase battery life.

There is one camera that seems to fit your desires.
At least it will give you a starting point.
It has a flash range of 12.4 feet.

Take a look at the Sony DSC-P73.

It has a 3X optical zoom and 4 megapixels, but still fits your price target.

A review is here:
http://www.steves-digicams.com/2004_reviews/p73.html


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