We all know and love the "I don't/couldn't give a f**k/shit/rat's ass" phrase. It helps a lot and relieves much tension. But would the rhetorical question form "What f**k do I give" be technically correct? I came up with this one time relying on my intuition with English. I've googled it and I saw that it indeed sees use, some apparently native speakers do use it in sentences.
Example of usage:
Jimmy: Hey, dad! I got an A on my math test.
Dad: Ok, Jimmy. But you need to answer to yourself a very important question.
Jimmy: What's that, dad?
Dad: What f**k do I give? The game's on and I'm watching. Now get the f**k outta here before I smack you.
Sorry for my morbid sense of humor, I hope it helped to get the point across :D