There is no such thing as an international patent application. However, it is possible to file a Paris Convention priority application in other countries within 1 year from the filing date in the U.S. Additionally, a patent application can be filed under the Patent Cooperation Treaty (PCT) within 1 year from the filing date in the U.S.
Both a Paris Convention priority application and a PCT patent application can claim the benefit of the filing date in the U.S. This is called a “priority date,” and if your foreign patent is later granted, the earlier filing date in the U.S. will be used to determine when your exclusive patent rights begin as described in https://www.jpost.com/Special-Content/Get-Your-Invention-Off-the-Ground-with-the-Support-of-InventHelp-624132 article.
A Paris Convention priority patent application is filed directly in foreign countries, and is immediately examined by the national patent office. A PCT patent application is delayed for some time in an international examination process. You can later enter into many countries for a lower price.
Most law firms charge an hourly rate for preparing a PCT application (plus a variable USPTO filing fee) from a complete utility patent application- the price depends upon the length and complexity of the original application. The cost of filing a PCT patent application from a provisional application will vary depending upon the extent of the provisional patent application as seen in https://spacecoastdaily.com/2020/03/inventhelp-the-way-forward-for-new-inventors/ post.