MailgunSample.cs

using System.Net.Http; // reference System.Net.Http.dll
using System.Net.Http.Headers;
using System.Threading.Tasks;

public static class MailgunSample
{
  public static async Task<string> SendSimpleMessageAsync(string domain, string apikey, string from, string to, string subject, string text)
  {
  	var authHeader = new AuthenticationHeaderValue("Basic",
  		Convert.ToBase64String(Encoding.ASCII.GetBytes($"api:{apikey}")));
  
  	var requestContent = new FormUrlEncodedContent(new Dictionary<string, string>
  	{
  		["from"] = from,
  		["to"] = to,
  		["subject"] = subject,
  		["text"] = text
  	});
  
  	using (var client = new HttpClient())
  	{
  		client.BaseAddress = new Uri("https://api.mailgun.net/v3/");
  		client.DefaultRequestHeaders.Authorization = authHeader;
  
  		using (var response = await client.PostAsync($"{domain}/messages", requestContent))
  			return await response.Content.ReadAsStringAsync();
  	}
  }
}