Question: GlobalMaximum of a function with various constraints.

Hey. Sorry if this is the wrong place to post, as I'm new here. Anyways, I'm trying to find the global maximum of a function, directly via Maple Commands, I've found that Maximize, does a good job to some degree, but when faced with "harder" constraints such as x^2+y^2=>1 it fails (or atleast I do :) ). I know that in WolframAlpha you can write that following as an example: 

Maximize[{(1-y^2)/(x^2), x^2 + y^2 <= 1,x>=1/2}, {x, y}],+x%5E2+%2B+y%5E2+%3C%3D+1,x%3E%3D1%2F2%7D,+%7Bx,+y%7D%5D

How would I do this in Maple? Any help would be more than welcome!! Thanks :D 

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