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I want to label the curves in Plot[] with their equations (eg. "y = x^2") not just their expressions (eg. x^2). There has to be a way to do this, but I cannot figure it out.

shadeBoundedRegion[top_, bottom_, a_, b_]:= Plot[{Max[top, bottom], top, bottom}, {x,a,b}, Filling -> {3 -> {1}}, PlotLabels->{"" ,Above,Above}];
shadeBoundedRegion[4,x^2,-3,3]

I apologize if this has been answered elsewhere, but I could not find it.

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Use PlotLabels -> {"", HoldForm[y = top], HoldForm[y = bottom]} in the definition of shadeBoundedRegion:

shadeBoundedRegion[top_, bottom_, a_, b_] :=  Plot[{Max[top, bottom], top, bottom}, 
 {x, a, b}, 
 Filling -> {3 -> {1}}, 
 PlotLabels -> {"", HoldForm[y = top], HoldForm[y = bottom]}];

shadeBoundedRegion[4, x^2, -3, 3]

enter image description here

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