How much is it approximately to repair a broken screen of a 2013 MacBook Pro?

Mac Repair - Official Apple Support

We are end users like you not Apple service advisors. It is my experience with calling Apple for pricing that they will not quote prices without examining the item, except for battery replacement cost which the publish on the support site.

That said, we do know that any problem with a Retina display requires replacing the entire assembly; it is a sealed unit and you can't simply replace the glass. Expect to hear a quote in the US$500-600 range.