print qq{ask_bigdb [options] >> $filename\n}; ### OFFENDING LINE!!!
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Suggestion:

my @lines = ask_bigdb(@options); # whatever that ask_bigdb is...
shift @lines;                    # get rid of header
open my $outfh, '>>', $filename  # append to file
   or die "Can't append to '$filename': $!\n";
print $outfh @lines;
close $outfh or die "Can't close '$filename': $!\n";
[download]

        redo;    # do the next arm of chromosome ...
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here's a mismatch between code and comment. Are you sure you want redo her, and not next?

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}