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Deadlifts (and maybe squats) are the best complex exertion one can do. We've claimed that ad nauseum. Which muscles do you want to stress with deadlifts? Core, glutes and hamstrings, legs, posterior chain, neck and trapezius. Got to go heavy.
Deadlifts are the best complex exertion, because as long as you don't break form you can go right to the edge of what you're physically capable of doing. They are a savage, simple lift. Failure (other than passing out) is relatively risk free--just let you.
Squats, while good, can't be pushed that far.
William O. B'Livion
I have failed my squats several times, both in the gym and in competition, and personally witnessed many more failures. In the gym I just lower the bar down to the safeties and get out from under the bar. In competition, I had spotters who helped me get the weight back in the supports. With the correct setup and perhaps a bit of practice, there is no danger to failing a squat. But yeah, just dropping the bar is certainly easier.
Why would you try to lift as much as you can? To prove something? Wouldn't it be easier to stuff a pair of rolled up socks in your pants to make it look like your dick was big? What are you trying to prove? Exercise should be to improve your physical health not to try to prove how much you can lift. Do three sets of 10 reps and the weight will be correct for you. Doing one rep and having to sit and recover is pure stupidity. If you can't do 10 reps you are lifting too much weight and you are going to hurt yourself. All to impress yourself or someone else.
You should look around and find a local competition, BD. Having a specific event to train for really focuses your attention and can lead to significant gains in your strength. Plus they are fun to participate in.