The difference between what you want and what you'll take is where you negotiate. The poker-playing part of negotiation comes into play. People usually start higher than what they really want. That's part of the way the game is played. However, be careful, if you ask too much, everybody just becomes angry.
Mediation is an organized form of negotiation.
Mediators train to help resolve disputes by helping frame credible positions and working to bring about understanding and, ultimately, compromise. Many lawyers and retired judges are mediators. Those are the rules. Know what you want, know what you'll take, believe in yourself and be reasonable. Your statement invites discussion of damaged machines and repair costs.