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I checked with the Product Manager and found out that we have not come across any specific limitations that would prevent a trial version of 3dcart integrating. Did you hear back from 3dcart on your inquiry?
I also just initiated a manual callback and the store now notates that a sync occurred. As such, I would recommend creating a new order in your store platform, making sure it is in a status we currently sync for your store, and then clicking the sync button on the Orders page in ShippingEasy to see if it comes through.
If the order still does not come through, please double check that you followed our integration guide exactly: How to: Integrate 3dcart with ShippingEasy and then provide the order number and corresponding status in the comment below so we can troubleshoot further.