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Default Sum a dynamically-defined range

I have a series of cells containing the defining limits of a range, i.e.:
-sheet name
-top row number
-top column number
-bottom row number
-bottom column number

How do I sum (or otherwise operate on) the array so defined? I have tried
formulae containing combinations of various ADDRESS and INDIRECT functions,
but have not yet come across one that works.

 
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