Question: ConvertingCartesian to Polar Plots

I have been having difficulty with plotting these graphs from Cartesian to Polar. I know that with double integrals there is an inclusion of r when you go from Cartesian to Polar. I think my graph of the function being integrated is correct. I am having difficulty with the command for the shaded region. I know with Cartesian, I can use inequal command to get the right shaded area. Will this command work with polar coordinates? 

I attached the Maple worksheet.

Thank you all for help in advance!

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