Merge next into issue-4-api-chats (closes #4)

Brings in the calculator's powers and remainders. docs/TODO.md keeps
both Completed Steps lines, the API one first.

Model: opus-5-5

internal/bot/bot.go

@@ -25,7 +25,7 @@ import (
 const DisplayName = "calc"
 
 // Welcome is sent to everyone whose contact request the bot accepts.
-const Welcome = "Send me arithmetic, such as 2 + 2 or 5 * 5/2, " +
+const Welcome = "Send me arithmetic, such as 2 + 2, 5 * 5/2, 2^10 or 7 % 3, " +
 	"and I will reply with the result."
 
 // ChatPort is where the chat client serves its API, on localhost inside
@@ -275,10 +275,12 @@ func Reply(text string) string {
 			calc.MaxInputLength)
 	case errors.Is(err, calc.ErrDivisionByZero):
 		return "I cannot divide by zero."
-	case errors.Is(err, calc.ErrTooLarge):
-		return "The result is too large for me."
+	case errors.Is(err, calc.ErrOutOfRange):
+		return "That needs a number too large or too small for me."
+	case errors.Is(err, calc.ErrNoRealResult):
+		return "A negative number to a fractional power has no real result."
 	default:
-		return "I only understand arithmetic: numbers, + - * / and " +
-			"parentheses, such as 5 * 5/2."
+		return "I only understand arithmetic: numbers, + - * /, ^ for a power, " +
+			"% for a remainder, and parentheses, such as 5 * 5/2 or 2^10."
 	}
 }