ModernMT is a translation service from Italy, which improves from corrections and adapts to the context of the whole document and not just the last sentence. The parent company Translated (also based in Italy) offers human reviewed translation and access to the machine translation API too.
It offers free machine translation for up to 5000 characters at a time. For enterprises, which might benefit from direct API access, the batch plan starts at $8 per million characters and for translators a model which adapts to your personal style would cost $25 a month.
Read more on the pricing page of the service.