Add support for letters (a, b, c, ...) in functions. So if the user types in sin(a) it should give back sin(a) as result not: sin(a) = Error: name 'a' is not defined. Also allow the user to define variables for example if the user types in a = 1 it should establish the variable a and give back a = 1 -> Variable defined. From that point on when ever the user types in a the program should interpreted it as the variable so in the example it would be sin(a) = sin(1). Also allow the user to change the variable by giving at a new value for example: a = 2. Python 3.12 Code: import math
import re
from typing import Any, Union, Callable
from math import ceil

from PySide6.QtWidgets import (
    QApplication, QMainWindow, QWidget, QVBoxLayout, QHBoxLayout,
    QLineEdit, QTextEdit, QScrollBar, QPushButton, QLabel, QFrame,
    QGridLayout
)
from PySide6.QtGui import QFont
from PySide6.QtCore import Qt

# -- Utility Functions --

def convert_angle(func: Callable[[float], float], x: float, use_degrees: bool) -> float:
    """Convert angle based on degree mode."""
    return func(math.radians(x) if use_degrees else x)

# -- Conversions Category --

def kilograms_to_pounds(kg: float) -> float:
    """Convert kilograms to pounds."""
    return kg / 0.45359237

def pounds_to_kilograms(lb: float) -> float:
    """Convert pounds to kilograms."""
    return lb * 0.45359237

def celsius_to_kelvin(c: float) -> float:
    """Convert Celsius to Kelvin."""
    return c + 273.15

def kelvin_to_celsius(k: float) -> float:
    """Convert Kelvin to Celsius."""
    return k - 273.15

def celsius_to_fahrenheit(c: float) -> float:
    """Convert Celsius to Fahrenheit."""
    return c * 9/5 + 32

def fahrenheit_to_celsius(f: float) -> float:
    """Convert Fahrenheit to Celsius."""
    return (f - 32) * 5/9

# -- Text Category --

def capitalize_sentence(sentence: str) -> str:
    """Capitalize the first letter of each word in the sentence."""
    return ' '.join(word.capitalize() for word in sentence.split())

def remove_duplicates(text: str) -> str:
    """Remove duplicate words and empty lines from a string."""
    words = ' '.join(line.strip() for line in text.splitlines() if line.strip()).split()
    return ' '.join(dict.fromkeys(words))

# -- Processing --

def get_safe_globals(use_degrees: bool) -> dict:
    """Return a dictionary of safe globals for expression evaluation."""
    trig_funcs = {'sin', 'cos', 'tan', 'asin', 'acos', 'atan'}
    safe_globals = {
        "sqrt": math.sqrt,
        "log": math.log10,
        "ln": math.log,
        "pi": math.pi,
        "e": math.e,
        "lb": kilograms_to_pounds,
        "kg": pounds_to_kilograms,
        "C": kelvin_to_celsius,
        "K": celsius_to_kelvin,
        "F": celsius_to_fahrenheit,
        "CF": fahrenheit_to_celsius,
        "capitalize": capitalize_sentence,
        "duplicates": remove_duplicates,
    }
    safe_globals.update({
        func: (lambda f: (lambda x, f=f: convert_angle(getattr(math, f), x, use_degrees)))(func)
        for func in trig_funcs
    })
    return safe_globals

def preprocess_text_functions(expression: str) -> str:
    """Preprocess text functions to ensure proper quoting of arguments."""
    def add_quotes(match):
        func, args = match.groups()
        return f'{func}("{args}")' if func in ['capitalize', 'duplicates'] else match.group(0)
    # Corrected regex pattern with only two capturing groups
    return re.sub(r'\b(capitalize|duplicates)\(([^)]+)\)', add_quotes, expression)

def validate_inverse_trig(expression: str, safe_globals: dict) -> Union[str, None]:
    """Validate inputs for inverse trigonometric functions."""
    for func, arg in re.findall(r"(\b\w+\b)\(([^)]+)\)", expression):
        if func in ["asin", "acos"]:
            try:
                value = eval(arg, {"builtins": None}, safe_globals)
                if abs(value) > 1:
                    return f"Error: {func}(x) is undefined for |x| > 1"
            except Exception as e:
                return f"Error: {e}"
    return None

def safe_evaluate(expression: str, safe_globals: dict, use_e_notation: bool) -> Union[str, Any]:
    """Safely evaluate the expression and format the result."""
    try:
        result = eval(expression, {"builtins": None}, safe_globals)
        if isinstance(result, float) and abs(result) < 1e-10:
            result = 0.0
        if isinstance(result, (int, float)):
            if use_e_notation:
                # Format using scientific notation with up to 2 decimal places
                result = f"{result:.2e}"
            else:
                # Standard formatting with rounding
                result = round(result, 2)
        return result
    except Exception as e:
        return f"Error: {e}"

def evaluate_expression(expression: str, use_degrees: bool = False, use_e_notation: bool = False) -> Union[float, str]:
    """Safely evaluate a mathematical expression considering degree mode."""
    safe_globals = get_safe_globals(use_degrees)
    expression = expression.replace("^", "**")
    expression = preprocess_text_functions(expression)
    error = validate_inverse_trig(expression, safe_globals)
    return error or safe_evaluate(expression, safe_globals, use_e_notation)

# -- GUI --

class CalculatorGUI(QMainWindow):
    """PySide6-based Calculator with Degrees/Radians toggle and history."""

    def __init__(self):
        super().__init__()
        self.use_degrees = False
        self.use_e_notation = False
        self.setup_window()
        self.create_widgets()
        self.layout_widgets()

    def setup_window(self) -> None:
        """Configure the main application window."""
        self.setWindowTitle("Calculator")
        self.setGeometry(100, 100, 1280, 720)

    def create_widgets(self) -> None:
        """Initialize all GUI components."""
        font = QFont()
        font.setPointSize(12)
        font.setFamily('Literata')

        self.entry = QLineEdit()
        self.entry.setFont(font)
        self.entry.returnPressed.connect(self.calculate)
        self.entry.setPlaceholderText('Enter expression')
        self.entry.setClearButtonEnabled(True)

        self.history_text = QTextEdit()
        self.history_text.setFont(font)
        self.history_text.setReadOnly(True)

        self.scrollbar = QScrollBar(Qt.Vertical)
        self.history_text.setVerticalScrollBar(self.scrollbar)

        self.function_buttons = {
            "Functions": ["sqrt", "sin", "cos", "tan", "asin", "acos", "atan", "log", "ln"],
            "Conversions": ["lb", "kg", "K", "C", "F", "CF"],
            "Text": ["capitalize", "duplicates"],
            "Constants": ["pi", "e"],
            "Settings": []
        }
        self.function_frame = QFrame()
        self.create_function_buttons(font)

    def create_function_buttons(self, font: QFont) -> None:
        """Create buttons for inserting functions into the entry."""
        layout = QGridLayout()

        # Updated col_span for "Settings" from 2 to 1
        categories = [("Functions", 3), ("Conversions", 2), ("Text", 2), ("Constants", 2), ("Settings", 1)]
        starting_col = 0

        for category, col_span in categories:
            label = QLabel(category)
            label.setFont(font)
            layout.addWidget(label, 0, starting_col, 1, col_span, Qt.AlignCenter)

            buttons = self.function_buttons.get(category, [])
            if category == "Functions":
                for i, func in enumerate(buttons):
                    button = QPushButton(func)
                    button.setFont(font)
                    button.clicked.connect(lambda _, f=func: self.insert_function(f, False))
                    layout.addWidget(button, (i // 3) + 1, starting_col + (i % 3))
            
            elif category == "Settings":
                # Arrange Settings buttons vertically within a single column
                self.mode_button = QPushButton("Radians")
                self.mode_button.setFont(font)
                self.mode_button.clicked.connect(self.toggle_mode)
                layout.addWidget(self.mode_button, 1, starting_col, 1, 1)

                self.e_notation_button = QPushButton("E Notation: Off")
                self.e_notation_button.setFont(font)
                self.e_notation_button.clicked.connect(self.toggle_e_notation)
                layout.addWidget(self.e_notation_button, 2, starting_col, 1, 1)
            
            elif category == "Conversions":
                for idx, func in enumerate(buttons):
                    if func == "lb":
                        display_text = "lb(kg)"
                    elif func == "kg":
                        display_text = "kg(lb)"
                    elif func == "K":
                        display_text = "K(°C)"
                    elif func == "C":
                        display_text = "°C(K)"
                    elif func == "F":
                        display_text = "F(°C)"
                    elif func == "CF":
                        display_text = "°C(F)"
                    else:
                        display_text = func
                    button = QPushButton(display_text)
                    button.setFont(font)
                    button.clicked.connect(lambda _, f=func: self.insert_function(f, False))
                    row = 1 + (idx // col_span)
                    col = starting_col + (idx % col_span)
                    layout.addWidget(button, row, col)
            
            else:
                num_buttons = len(buttons)
                num_rows = ceil(num_buttons / col_span)

                for idx, func in enumerate(buttons):
                    button_text = f"{func}"
                    button = QPushButton(button_text)
                    button.setFont(font)
                    button.clicked.connect(lambda _, f=func, c=(category == "Constants"): self.insert_function(f, c))
                    row = 1 + (idx // col_span)
                    col = starting_col + (idx % col_span)
                    layout.addWidget(button, row, col)

                for extra in range(col_span * num_rows - num_buttons):
                    layout.addWidget(QLabel(""), 1 + (extra // col_span), starting_col + (extra % col_span))

            starting_col += col_span

        self.function_frame.setLayout(layout)

    def layout_widgets(self) -> None:
        """Arrange widgets within the window."""
        central_widget = QWidget()
        main_layout = QVBoxLayout()

        main_layout.addWidget(self.entry)

        history_layout = QHBoxLayout()
        history_layout.addWidget(self.history_text)
        history_layout.addWidget(self.scrollbar)
        main_layout.addLayout(history_layout)

        main_layout.addWidget(self.function_frame)

        central_widget.setLayout(main_layout)
        self.setCentralWidget(central_widget)

    def toggle_mode(self) -> None:
        """Switch between Degrees and Radians modes."""
        self.use_degrees = not self.use_degrees
        self.mode_button.setText("Degrees" if self.use_degrees else "Radians")

    def toggle_e_notation(self) -> None:
        """Toggle the E notation setting."""
        self.use_e_notation = not self.use_e_notation
        state = "On" if self.use_e_notation else "Off"
        self.e_notation_button.setText(f"E Notation: {state}")

    def insert_function(self, function: str, is_constant: bool = False) -> None:
        """Insert function or constant text into the expression entry."""
        current_text = self.entry.text()
        cursor_position = self.entry.cursorPosition()
        if is_constant:
            new_text = f"{current_text[:cursor_position]}{function}{current_text[cursor_position:]}"
            new_cursor_position = cursor_position + len(function)
        else:
            new_text = f"{current_text[:cursor_position]}{function}() {current_text[cursor_position:]}"
            new_cursor_position = cursor_position + len(function) + 1
        self.entry.setText(new_text)
        self.entry.setCursorPosition(new_cursor_position)
        self.entry.setFocus()

    def calculate(self) -> None:
        """Evaluate the expression and update history."""
        expression = self.entry.text().strip()
        if expression:
            result = evaluate_expression(expression, use_degrees=self.use_degrees, use_e_notation=self.use_e_notation)
            self.display_result(expression, result)
            self.entry.clear()

    def display_result(self, expression: str, result: Union[float, str]) -> None:
        """Append the calculation to the history log."""
        mode = "D" if self.use_degrees else "R"
        self.history_text.append(f"[{mode}] {expression} = {result}")
        self.history_text.verticalScrollBar().setValue(
            self.history_text.verticalScrollBar().maximum()
        )

def main() -> None:
    """Run the Calculator application."""
    app = QApplication([])
    calculator = CalculatorGUI()
    calculator.show()
    app.exec()

if __name__ == "__main__":
    main()