Simple examples to open a file for reading:

        open(my $fh, "<", "input.txt")
    	or die "Can't open < input.txt: $!";

and for writing:

        open(my $fh, ">", "output.txt")
    	or die "Can't open > output.txt: $!";

##</code><code>##

while (<$input>) {
    chomp;
    # do something with $_
}

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

my $filename = 'counts.txt';

open (my $fh, '+<', $filename)
    or die "Could not open '$filename' $!";

my $count = "";

while (<$fh>) {
    chomp;
    if ($_ =~ /^>hsa/) {
	$count .= length $_;
        $count .= " ";
    }
}

print $fh $count . "\n";
close $fh
    or die "Could not close '$filename' $!";

__END__

>hsa_circ_0000001|chr1:1080738-1080845-|None|None
ATGGGGTTGGGTCAGCCGTGCGGTCAGGTCAGGTCGGCCATGAGGTCAGGTGGGGTCGGCCATGAAGGTGGTGGGGGTCATGAGGTCACAAGGGGGTCGGCCATGTG
>hsa_circ_0000002|chr1:1158623-1159348-|NM_016176|SDF4
GGTGGATGTGAACACTGACCGGAAGATCAGTGCCAAGGAGATGCAGCGCTGGATCATGGAGAAGACGGCCGAGCACTTCCAGGAGGCCATGGAGGAGAGCAAGACACACTTCCGCGCCGTGGACCCTGACGGGGACGGTCACGTGTCTTGGGACGAGTATAAGGTGAAGTTTTTGGCGAGTAAAGGCCATAGCGAGAAGGAGGTTGCCGACGCCATCAGGCTCAACGAGGAACTCAAAGTGGATGAGGAAA
49 54

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

my $filename = 'counts.txt';

open (my $fh, '+<', $filename)
    or die "Could not open '$filename' $!";

chomp(my @lines = <$fh>);

for (@lines) { print $fh length($_) . " " if ($_ =~ /^>hsa/); }

close $fh
    or die "Could not close '$filename' $!";

__END__

>hsa_circ_0000001|chr1:1080738-1080845-|None|None
ATGGGGTTGGGTCAGCCGTGCGGTCAGGTCAGGTCGGCCATGAGGTCAGGTGGGGTCGGCCATGAAGGTGGTGGGGGTCATGAGGTCACAAGGGGGTCGGCCATGTG
>hsa_circ_0000002|chr1:1158623-1159348-|NM_016176|SDF4
GGTGGATGTGAACACTGACCGGAAGATCAGTGCCAAGGAGATGCAGCGCTGGATCATGGAGAAGACGGCCGAGCACTTCCAGGAGGCCATGGAGGAGAGCAAGACACACTTCCGCGCCGTGGACCCTGACGGGGACGGTCACGTGTCTTGGGACGAGTATAAGGTGAAGTTTTTGGCGAGTAAAGGCCATAGCGAGAAGGAGGTTGCCGACGCCATCAGGCTCAACGAGGAACTCAAAGTGGATGAGGAAA
49 54

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

my $count;
while (<>) {
    if ($_ =~ /^>hsa/){
	chomp (my $line = <>);
	$count .= length($line);
        $count .= " ";
	print "Count final: " . $count . "\n";
    }
} continue {
    close ARGV if eof; # reset $. each file
}

my $filename = 'counts.txt';

open (my $fh, '>', $filename)
    or die "Could not open '$filename' $!";

print $fh $count;

close $fh
    or die "Could not close '$filename' $!";

__END__

$ perl test.pl test.txt
Count final: 107
Count final: 107 251

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

my $filename = 'counts.txt';

open (my $fh, '>', $filename)
    or die "Could not open '$filename' $!";

chomp(my @lines = <>);

for (@lines) {
    next if ($_ =~ /^>hsa/);
    print $fh length($_) . " ";
}

print $fh "\n";

close $fh
    or die "Could not close '$filename' $!";

__END__

$ cat counts.txt
107 251

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

my $filename = 'counts.txt';

open (my $fh, '>', $filename)
    or die "Could not open '$filename' $!";

chomp(my @lines = <>);

for (@lines) { print $fh length($_) . " " if ($_ =~ tr/ACGT//); }

print $fh "\n";

close $fh
    or die "Could not close '$filename' $!";

__END__

$ cat counts.txt
107 251