Custom pricing for a service based on geographical location

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We have our own Pricing API that we would like to hook up to Shopify.

The user would select a service from our list of services, input some geographical locations of where this service would be performed, select a date.  After that, we want that info sent to our pricing model which will return a price & price token.  The user would then agree to this price and checkout using Shopify.  Is that something that could be done.  If yes, where and how can we customize this feature?