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Hello, I have two problems.

the first is plotting 3D function, the domain is "0<x<y<1". (I could find examples like integrating function with domain 0<x<1, 0<y<1, but I could not find examples for a<x<y<b.)

the second is just Intergrating the funcntion below.

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For the plot you can use RegionFunction, which takes a pure function which takes x, y, and z values::

Plot3D[1/(1-x),{x,0,1},{y,0,1},RegionFunction->Function[{x,y,z},x<y]]

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Your second issue is fixed by spelling Integrate properly (notice that Intergrate is in blue, meaning that it is an undefined global variable), and by swapping the order of integration:

Integrate[Sqrt[x^2+y^2]/Pi, {x, 0, 1}, {y, -Sqrt[1-x^2], Sqrt[1-x^2]}]

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    $\begingroup$ Also, Plot3D[1/(1 - x), {x, 0, 1}, {y, x, 1}] $\endgroup$
    – Bob Hanlon
    May 26 at 0:05
  • $\begingroup$ Wow... I had so many mistakes, really really thanks. $\endgroup$
    – jerryed
    May 26 at 2:25

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