Rewrite `io::BufRead` doc examples to better demonstrate behaviors.

Prior to this commit, most of the `BufRead` examples used `StdinLock` to
demonstrate how certain `BufRead` methods worked. Using `StdinLock` is
not ideal since:

* Relying on run-time data means we can't show concrete examples of how
  these methods work up-front. The user is required to run them in order
  to see how they behave.
* If the user tries to run an example in the playpen, it won't work
  because the playpen doesn't support user input to stdin.

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