Question: How to calculate the area of this closed area?

I am a Mathematica user actually. And I can know x^(1/(x + 1/x)) + y^(1/(y + 1/y)) == E is closed by the code:

ContourPlot[x^(1/(x + 1/x)) + y^(1/(y + 1/y)) == E, {x, 0, 7}, {y, 0, 7}]

But Mathematica cannot calculate this integral Integrate[1,Element[{x,y},ImplicitRegion[x^(1/(x+1/x))+y^(1/(y+1/y))>=E,{{x,0,7},{y,0,7}}]]]. It just can give a numerical solution by NIntegrate, This makes me depressed. So I try to calculate it by Maple. After I read some documentation of maple, I don't know how to use a implicit function to expression a region to do integral in MultiInt. So I ask here to help. Anybody can tell me how to write this code in Maple?

Please Wait...