Is it better to do the maximum weight for that number of reps as far as possible or start lower and stay at that weight for the entire set?
For strength, your best bet is low reps (2 to 5 per set), long rest periods (2 minutes +) and low volume (e.g. 3 to 4 sets).
For muscle mass, moderate reps (6 to 12 reps per set), moderate rest (1 - 2 minutes) and moderate to high volume, depending on intensity (5 to 8 sets).
For endurance, high reps (15+), brief rest (30 seconds to 1 minute), and moderate to high volume (5 to 10 sets).
These are VERY general guidelines, keep in mind. The specifics of a program will vary a lot.
I find both approaches to weight that you mention work well.
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And see every new exercise and training technique the moment I load it up!