I don't think that toolic's approach could be improved upon, but that doesn't mean we shouldn't be able to have a little fun. ;)

use feature qw(state);

tally(\*DATA);

sub tally {
  my $fh = shift;
  state $acc = 0;
  return if ! defined( local $_ = <$fh> );
  $acc += ( my( $n, $d ) = split )[0];
  printf "%-5d %s\n", $acc, $d;
  tally($fh);
}

__DATA__
1   2005-01-16
6   2005-01-28
1   2005-01-31
2   2005-02-01
2   2005-02-02
1   2005-02-05
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One possible "improvement" to this one: Tie $n to a class that increments upon STORE, and you can eliminate state $acc, just using $n as the accumulator. :)