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Our entire programme is now down to 28 lines with appropriate whitespace, and supports much more than your original did. (Your original was 44 lines.)

Our entire programme is now down to 29 lines with appropriate whitespace, and supports much more than your original did. (Your original was 44 lines.)

Our entire programme is now down to 26 lines with appropriate whitespace, and supports much more than your original did. (Your original was 44 lines.)

var prompter = new ConsolePrompt(null);

Console.WriteLine("Hello, welcome to Alex's basic calculator!");
Console.ReadLine();

var operations = new Dictionary<string, Func<double, double, double>>
{
    {"x", (x, y) => x * y },
    {"/", (x, y) => x / y },
    {"+", (x, y) => x + y },
    {"-", (x, y) => x - y },
    {"^", (x, y) => Math.Pow(x, y) },
    {"%", (x, y) => x % y }
};

do
{
    var firstNum = prompter.Prompt<double>("Enter the first number in your basic equation", PromptOptions.Required);
    var secondNum = prompter.Prompt<double>("Enter the second number in your basic equation", PromptOptions.Required);
    var operation = prompter.Prompt<string>("Ok now enter your operation (" + string.Join(", ", operations.Keys) + ")", PromptOptions.Required, null, null, x => operations.Keys.Contains(x));

    var answer = operations[operation](firstNum, secondNum);

    Console.WriteLine($"{firstNum} {operation} {secondNum} = {answer}");
    Console.ReadLine();
} while (prompter.Prompt("Enter exit to quit, anything else to continue", PromptOptions.Optional, "", parseResultMethod: x => x.ToLowerInvariant()) != "exit");

Lastly, as for a bonus to this answer, you can also add alias operations. (What do I mean? Well what if I naturally use * instead of x for multiplication?)

This is super easy:

// Let's add our alias operations, */x
operations.Add("*", (x, y) => operations["x"](x, y));

Simply add them after the var operations statement.

var operations = new Dictionary<string, Func<double, double, double>>
{
    {"x", (x, y) => x * y },
    {"/", (x, y) => x / y },
    {"+", (x, y) => x + y },
    {"-", (x, y) => x - y },
    {"^", (x, y) => Math.Pow(x, y) },
    {"%", (x, y) => x % y }
};

// Let's add our alias operations, */x
operations.Add("*", (x, y) => operations["x"](x, y));

Boom, now you can use * instead of x for multiplication. (But you can still use x as well.)

Our entire programme is now down to 28 lines with appropriate whitespace, and supports much more than your original did. (Your original was 44 lines.)

var prompter = new ConsolePrompt(null);

Console.WriteLine("Hello, welcome to Alex's basic calculator!");
Console.ReadLine();

var operations = new Dictionary<string, Func<double, double, double>>
{
    {"x", (x, y) => x * y },
    {"/", (x, y) => x / y },
    {"+", (x, y) => x + y },
    {"-", (x, y) => x - y },
    {"^", (x, y) => Math.Pow(x, y) },
    {"%", (x, y) => x % y }
};

// Let's add our alias operations, */x
operations.Add("*", (x, y) => operations["x"](x, y));

do
{
    var firstNum = prompter.Prompt<double>("Enter the first number in your basic equation", PromptOptions.Required);
    var secondNum = prompter.Prompt<double>("Enter the second number in your basic equation", PromptOptions.Required);
    var operation = prompter.Prompt<string>("Ok now enter your operation (" + string.Join(", ", operations.Keys) + ")", PromptOptions.Required, null, null, x => operations.Keys.Contains(x));

    var answer = operations[operation](firstNum, secondNum);

    Console.WriteLine($"{firstNum} {operation} {secondNum} = {answer}");
    Console.ReadLine();
} while (prompter.Prompt("Enter exit to quit, anything else to continue", PromptOptions.Optional, "", parseResultMethod: x => x.ToLowerInvariant()) != "exit");

var validOperations = new[] { "x", "/", "+", "-" };
var firstNum prompter.Prompt<int>("Enter the first number in your basic equation", PromptOptions.Required);
var secondNum = prompter.Prompt<int>("Now enter your second number in the basic equation", PromptOptions.Required);
var operation = prompter.Prompt<string>("Ok now enter your operation (" + string.Join(", ", validOperations) + ")", PromptOptions.Required, null, null, x => validOperations.Contains(x));

var validOperations = new[] { "x", "/", "+", "-" };
var firstNum prompter.Prompt<int>("Enter the first number in your basic equation", PromptOptions.Required);
var secondNum = prompter.Prompt<int>("Now enter your second number in the basic equation", PromptOptions.Required);
var operation = prompter.Prompt<string>("Ok now enter your operation (" + string.Join(", ", validOperations) + ")", PromptOptions.Required, validationMethod: x => validOperations.Contains(x));