A few, several, a lot of express relative quantities, not absolute quantities. They scale to the speaker's and hearer's understanding of what is normal or is contextually requuired.
For instance, if you say “Most of our people have tablets; only a few still work off of towers”, a few may mean three or five or six if you work for a small business, but fifty or a hundred if you work for a large national enterprise. “We've only got a few teaspoons” may mean three or four if you’re inviting friends over for dinner, twenty or thirty if you’re planning a banquet.
Similarly, “There are several approaches to this problem” might mean four or eight; but “Several recent papers have offered approaches to this problem” might be twenty or more in a busy academic field.