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number types

    I feel sort of silly asking something that should be so clear but after
LOTS of trying I can't seem to get it right.

How can I make Mathematica know that a variable is real or positive so that

Conjugate[a] gives a

Sqrt[ a^2 ] gives a

when I evaluate integrals with a in them it doesn't give me an If statement

If[ Im[a]=0, answer I want   , unevaluated integral ]

    this seems like it should be easy but I nothing that I try ever works.

Thanks for any help.

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