编写程序，实现加减乘除、平方和开方计算。(Java语言)

在Java中，我们可以创建一个名为`Calculator`的类，然后通过继承和重写抽象方法来实现加减乘除、平方和开方的功能。这里是一个简单的例子：

import java.lang.Math;

abstract class BasicMathOperation {
    abstract double performOperation(double a, double b);
}

class Calculator extends BasicMathOperation {
    @Override
    public double add(double a, double b) {
        return a + b;
    }

    @Override
    public double subtract(double a, double b) {
        return a - b;
    }

    @Override
    public double multiply(double a, double b) {
        return a * b;
    }

    @Override
    public double divide(double a, double b) {
        if (b != 0) {
            return a / b;
        } else {
            throw new IllegalArgumentException("Division by zero is not allowed.");
        }
    }

    // 平方函数
    public double square(double num) {
        return Math.pow(num, 2);
    }

    // 开方函数
    public double squareRoot(double num) {
        if (num >= 0) {
            return Math.sqrt(num);
        } else {
            throw new IllegalArgumentException("Cannot calculate square root of a negative number.");
        }
    }
}

public class Main {
    public static void main(String[] args) {
        Calculator calculator = new Calculator();
        System.out.println("Addition: " + calculator.add(5, 3));
        System.out.println("Subtraction: " + calculator.subtract(10, 4));
        System.out.println("Multiplication: " + calculator.multiply(6, 2));
        System.out.println("Division: " + calculator.divide(15, 5));

        System.out.println("Square: " + calculator.square(4));
        System.out.println("Square Root: " + calculator.squareRoot(9));
    }
}

在这个程序中，`Calculator`类实现了`BasicMathOperation`接口，并提供了各种数学操作的具体实现。在`main`方法中，我们创建了一个`Calculator`实例并进行了计算。