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I was making the lid of the Starbucks cup and this problem occurs to me. I don't have a clear idea how to make the notch on the lid for drinking. Knowing about the knife tool I gave myself a try, with the tool cutting edges on the surface. And here comes my result:

with knife tool

But I don't think that's a perfect solution because when SubSurf is applied to it, the normals of the vertical part around the notch don't seem as perfect as the other vertical parts, with some uneven feeling:

uneven after subsurf

Meanwhile, if I want to give it Solidify, some black parts appeared:

some black parts

I'm a beginner in Blender for a week or two and I'm still praticing modeling after some basic learning from BlenderGuru. Any suggestion is appreciated!

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You could do it with this topology, at the beginning use i to inset. Then you can add some edge loops if you want to be more precise...

enter image description here

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