There are many. Sed is fast. This will give you lines 11 to 500

sed -n '11,500p' < file.txt

Man pages can be tricky as the content can vary distro by distro (how up to date is your copy of man-pages, what changes have happened, etc.) - this technique is pretty portable to extract the synopsis of a man page specifically due to the format it uses (most times I'd use like grep -A3 -B2 foo /some/file, e.g.).

Calling cut with a newline as the field delimiter works:

man systemd | cut -d $'\n' -f 4

Works with multiple lines too:

cut -d $'\n' -f 10-20,50-60