002: my $page = 1;
and
007:    my $start = ($page - 1) * 10;

#!/usr/bin/perl
use 5.014;
# 972560

my $page = 1; 
my $start = ($page - 1) * 10;   # please recite the rules on 
                                # evaluation order and the zero-times 
+table
my $end   = $start + 10;

say "\$start: $start; \$end: $end";
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Output:

Is there something wrong with my logic?

What do you think this does  my $page = 1; ?

I'm not sure what the while loop is for if you only want to show one page. Here is slightly refactored code with it removed.

sub browse_ten {

  # work out how many users
  my @users = glob("users_dir/*");
  my $no_of_users = scalar(@users);
  
  # calculate how many pages to display
  my $page_last = ceil($no_of_users / 10) ; 
  
  # get page to show from param or default 1
  my $page_show = param('page') || 1;
  my $page_prev = $page_show - 1;
  my $page_next = $page_show + 1;

  # decide whether to show links
  print h2("Page $page_show of $page_last"); # optional
  if ($page_show > 1) {
    # Show a Previous link
    print a({href => "?page=$page_prev"},"Previous");
  }
    
  if ($page_show < $page_last) {
    # Show a Next link
    print a({href => "?page=$page_next"},"Next");
  }
  
  # calc start and end user index number starting
  # page 1 user start is 0, page 2 is 10 
  # page 1 end is start + 9 unless on last page
  my $user_start = ($page_show - 1) * 10;
  my $user_end = ($page_show < $page_last) ? $user_start + 9 : $no_of_
+users - 1 ;

  # Show the range of entries.
  for my $i ($user_start .. $user_end) {
    my $user_to_show = $users[$i]; 
    
    # user image
    my $img_src = "$user_to_show/image.jpg";
    unless (-r $img_src){
      $img_src = 'blank_profile.jpg';
    }
    print img({src =>$img_src, width=>150, height=> 150 });
   
    # user profile
    my $profile_filename = "$user_to_show/profile";
    if (open my $p, $profile_filename){ 
      my $profile = join '<br/>', <$p>;
      close $p;
      print $profile;
    } else {
      print "Can not open $profile_filename : $!";
    }  
    print br;
  }
}
[download]